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Luca Benvenuti
Department of Computer, Control, and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185, Roma, Italy

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Journal article
Published: 10 June 2021 in Journal of Cleaner Production
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In this work, a set of diet plans that are nutritionally adequate and healthy, affordable, and environmentally friendly is analyzed. They refer to two-week full-board menus for nursing homes and are designed using a multi-objective optimization model in which different conflicting goals, such as the carbon and water footprints, cost, and nutritional and acceptability requirements, are pursued. As a consequence, the design provides a set of several menus corresponding to different trade-offs between the goals. Energy and nutrient contents are constrained in suitable ranges suggested by the dietary recommendation of health authorities. The carbon and water footprints and the cost of the diet are considered as goals to be minimized. More than one hundred menus have been considered to explore all the possible trade-offs between the three goals. The analysis shows that cheaper menus are more environmentally impacting and that it is possible to make a trade-off between the carbon and water footprints while keeping the cost of the menu unchanged. Moreover, it is possible to quantify the cost increase for a given improvement either of the carbon or water footprint. On the other hand, all the menus are nutritionally adequate and, more importantly, energy and nutrient contents are almost the same despite the large differences in their carbon and water footprints, and cost. Another interesting result of this study is the analysis of the relationships between the energy and nutrient intakes of the optimal menus and their cost and environmental impacts.

ACS Style

Luca Benvenuti; Alberto De Santis; Paola Cacchione. Multi-indicator design and assessment of sustainable diet plans. Journal of Cleaner Production 2021, 313, 127699 .

AMA Style

Luca Benvenuti, Alberto De Santis, Paola Cacchione. Multi-indicator design and assessment of sustainable diet plans. Journal of Cleaner Production. 2021; 313 ():127699.

Chicago/Turabian Style

Luca Benvenuti; Alberto De Santis; Paola Cacchione. 2021. "Multi-indicator design and assessment of sustainable diet plans." Journal of Cleaner Production 313, no. : 127699.

Journal article
Published: 07 May 2021 in Nutrients
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School is considered a privileged environment for health education and school feeding represents an opportunity for promoting sustainable foods to young generations. The objective of this paper is to demonstrate that is possible to select, from existing school menus, recipes that combine healthy foods with low environmental impact. A national sample of Italian school menus was collected and a total number of 194 recipes were included on a database containing 70 first courses, 83 s courses, 39 side dishes, 1 portion of fruit, and 1 portion of bread. A mathematical model was conceived to combine nutritional adequacy and acceptability criteria while minimizing GHGs emissions. The result is a four-week menu characterized by large vegetable components that were used not only as side dishes but also as ingredients in the first and second courses. Legumes and pasta are often included, and white meat is selected instead of red meat. The findings presented in this paper demonstrated that it is possible to design environmental-friendly meals from existing school menus. The mathematical model developed in this work has the potentiality of being completely scalable, easily updatable, and widely utilizable in different settings either for design or monitoring purposes as well as for research data collection.

ACS Style

Laura Rossi; Marika Ferrari; Deborah Martone; Luca Benvenuti; Alberto De Santis. The Promotions of Sustainable Lunch Meals in School Feeding Programs: The Case of Italy. Nutrients 2021, 13, 1571 .

AMA Style

Laura Rossi, Marika Ferrari, Deborah Martone, Luca Benvenuti, Alberto De Santis. The Promotions of Sustainable Lunch Meals in School Feeding Programs: The Case of Italy. Nutrients. 2021; 13 (5):1571.

Chicago/Turabian Style

Laura Rossi; Marika Ferrari; Deborah Martone; Luca Benvenuti; Alberto De Santis. 2021. "The Promotions of Sustainable Lunch Meals in School Feeding Programs: The Case of Italy." Nutrients 13, no. 5: 1571.

Methods
Published: 06 November 2020 in Frontiers in Nutrition
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Background: Food consumption is one of the most important drivers of the relation between human well-being and Earth's ecosystems. The current production level is difficult to sustain without compromising environmental integrity or public health. This calls for a decisive change in food consumption patterns in order to improve nutrition quality while respecting biodiversity and ecosystems. This change will produce some effect only if it is also culturally acceptable, accessible, economically fair and affordable. The design of food plans is traditionally carried out using mathematical optimization models, such as linear programming. This method has proved to be successful in providing nutritionally adequate diets while minimizing their economic and environmental impact. Nevertheless, cultural habits as well as attractiveness and variety of meals is very difficult to deal with, and no fully satisfactory way to include these issues in linear programming has been found. Objective: The aim of this paper is to move from traditional linear programming to a new programming methodology in order to cope also with acceptability in the design of meal plans. Method: Binary integer linear programming is the new modeling paradigm. In the proposed model, meal plans consist of providing the sequence and composition of daily meals over a given period of time and each meal can be composed using dishes from a given set. Therefore, instead of defining just a level of consumption of food groups or food items, the proposed model provides a realistic menu. To cope with sustainability, the energy and nutritional content of each dish is calculated together with its price and environmental impact. Furthermore, acceptability can be explicitly taken into account in a very natural way, that is bounding the daily, weekly, or total repetitions of single dishes and of dishes in the same food groups. Results: The paper reviews three successful studies with increasing complexity considering lunch plans for schools and full-board menus for nursing homes. The case studies show a great reduction of the environmental impact of the meal plans while ensuring an adequate nutritional intake, affordable prices and most importantly the plans are varied and culturally acceptable.

ACS Style

Luca Benvenuti; Alberto De Santis. Making a Sustainable Diet Acceptable: An Emerging Programming Model With Applications to Schools and Nursing Homes Menus. Frontiers in Nutrition 2020, 7, 1 .

AMA Style

Luca Benvenuti, Alberto De Santis. Making a Sustainable Diet Acceptable: An Emerging Programming Model With Applications to Schools and Nursing Homes Menus. Frontiers in Nutrition. 2020; 7 ():1.

Chicago/Turabian Style

Luca Benvenuti; Alberto De Santis. 2020. "Making a Sustainable Diet Acceptable: An Emerging Programming Model With Applications to Schools and Nursing Homes Menus." Frontiers in Nutrition 7, no. : 1.

Journal article
Published: 12 September 2020 in Systems & Control Letters
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In some applications one is interested in having a state–space realization with nonnegative matrices (positive realization) of a given transfer function and it is known that such a realization may have a dimension strictly larger than the order of the transfer function itself. Moreover, in most cases, it is desirable to have a realization with minimal dimension. Unfortunately, it is not known, to date, how to determine in general the minimum dimension of a positive realization and only lower and upper bounds to it are available. This letter provides an upper bound on the dimension of a minimal positive realization for transfer functions with simple poles. This is a considerable improvement on an earlier upper bound in which only transfer functions with real poles were considered.

ACS Style

Luca Benvenuti. An upper bound on the dimension of minimal positive realizations for discrete time systems. Systems & Control Letters 2020, 145, 104779 .

AMA Style

Luca Benvenuti. An upper bound on the dimension of minimal positive realizations for discrete time systems. Systems & Control Letters. 2020; 145 ():104779.

Chicago/Turabian Style

Luca Benvenuti. 2020. "An upper bound on the dimension of minimal positive realizations for discrete time systems." Systems & Control Letters 145, no. : 104779.

Original research article
Published: 04 May 2020 in Frontiers in Nutrition
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Objective: The aim of this study is to define a healthy and sustainable diet model with low GHGE, fulfilling dietary requirements, and considering current Italian food consumption patterns. Design: A duly designed database was developed, linking food nutritional composition and GHGE based on 921 food items consumed in Italy according to the last national food consumption survey (INRAN-SCAI 2005–2006). Linear programming was used to develop new diet plans separately for males and females, aged 18–60 years (n = 2,098 subjects), in order to minimize GHGE. The program is based on dietary goals and acceptability constraints as well as on 13 nutrient requirement constraints aiming to reach a healthy and acceptable diet for the Italian population. Results: Diet optimization resulted in a nutritionally adequate pattern minimizing GHGE values (4.0 vs. 1.9 kg CO2e/day for males and 3.2 vs. 1.6 kg CO2e/day for females). In both sexes, the nutrient intake of the optimized diet was at the established lower bound for cholesterol and calcium and at the established upper bound for free sugar and fiber. In males, intake of zinc was at the established lower bound whereas iron was at the established upper bound. Consumption of red meat and fruit and vegetables was at the established lower and upper bound, respectively, in both males and females. Despite the decrease in meat consumption, especially red meat, in the optimized diet with respect to the observed diet, levels of iron intake in females increased by 10% (10.3 vs. 11.3 mg/day) but remained below the adequate intake established in Italian national DRIs. Conclusions: An attainable healthy dietary pattern was developed that would lead to the reduction of GHGE by 48% for males and by 50% for females with respect to current food consumption in the Italian adult population. Health-promoting dietary patterns can substantially contribute to achieve related Sustainable Development Goals.

ACS Style

Marika Ferrari; Luca Benvenuti; Laura Rossi; Alberto De Santis; Stefania Sette; Deborah Martone; Raffaela Piccinelli; Cinzia Le Donne; Catherine Leclercq; Aida Turrini. Could Dietary Goals and Climate Change Mitigation Be Achieved Through Optimized Diet? The Experience of Modeling the National Food Consumption Data in Italy. Frontiers in Nutrition 2020, 7, 48 .

AMA Style

Marika Ferrari, Luca Benvenuti, Laura Rossi, Alberto De Santis, Stefania Sette, Deborah Martone, Raffaela Piccinelli, Cinzia Le Donne, Catherine Leclercq, Aida Turrini. Could Dietary Goals and Climate Change Mitigation Be Achieved Through Optimized Diet? The Experience of Modeling the National Food Consumption Data in Italy. Frontiers in Nutrition. 2020; 7 ():48.

Chicago/Turabian Style

Marika Ferrari; Luca Benvenuti; Laura Rossi; Alberto De Santis; Stefania Sette; Deborah Martone; Raffaela Piccinelli; Cinzia Le Donne; Catherine Leclercq; Aida Turrini. 2020. "Could Dietary Goals and Climate Change Mitigation Be Achieved Through Optimized Diet? The Experience of Modeling the National Food Consumption Data in Italy." Frontiers in Nutrition 7, no. : 48.

Journal article
Published: 20 January 2020 in The Electronic Journal of Linear Algebra
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The nonnegative inverse eigenvalue problem is the problem of determining necessary and sufficient conditions for a multiset of complex numbers to be the spectrum of a nonnegative real matrix of size equal to the cardinality of the multiset itself. The problem is longstanding and proved to be very difficult so that several variations have been defined by considering particular classes of multisets and nonnegative real matrices. In this paper, a novel variation of the problem is proposed. This variation is motivated by a practical application in the positive realization problem, that is the problem of characterizing existence and minimality of a positive state--space representation of a given transfer function.

ACS Style

Luca Benvenuti. The NIEP and the positive realization problem. The Electronic Journal of Linear Algebra 2020, 36, 367 -384.

AMA Style

Luca Benvenuti. The NIEP and the positive realization problem. The Electronic Journal of Linear Algebra. 2020; 36 (36):367-384.

Chicago/Turabian Style

Luca Benvenuti. 2020. "The NIEP and the positive realization problem." The Electronic Journal of Linear Algebra 36, no. 36: 367-384.

Journal article
Published: 09 December 2019 in Systems & Control Letters
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In some applications, one is interested in having a state–space realization with nonnegative matrices (positive realization) of a given transfer function and it is known that such a realization may have a dimension strictly larger than the order of the transfer function itself. The aim of this letter is to provide a lower bound on the minimum dimension of a positive realization taking into account some spectral properties of nonnegative matrices.

ACS Style

Luca Benvenuti. A lower bound on the dimension of minimal positive realizations for discrete time systems. Systems & Control Letters 2019, 135, 104595 .

AMA Style

Luca Benvenuti. A lower bound on the dimension of minimal positive realizations for discrete time systems. Systems & Control Letters. 2019; 135 ():104595.

Chicago/Turabian Style

Luca Benvenuti. 2019. "A lower bound on the dimension of minimal positive realizations for discrete time systems." Systems & Control Letters 135, no. : 104595.

Journal article
Published: 01 November 2019 in Journal of Cleaner Production
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ACS Style

Luca Benvenuti; Alberto De Santis; Andrea Di Sero; Nicola Franco. Concurrent economic and environmental impacts of food consumption: are low emissions diets affordable? Journal of Cleaner Production 2019, 236, 1 .

AMA Style

Luca Benvenuti, Alberto De Santis, Andrea Di Sero, Nicola Franco. Concurrent economic and environmental impacts of food consumption: are low emissions diets affordable? Journal of Cleaner Production. 2019; 236 ():1.

Chicago/Turabian Style

Luca Benvenuti; Alberto De Santis; Andrea Di Sero; Nicola Franco. 2019. "Concurrent economic and environmental impacts of food consumption: are low emissions diets affordable?" Journal of Cleaner Production 236, no. : 1.

Journal article
Published: 01 February 2019 in The Electronic Journal of Linear Algebra
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The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of determining necessary and sufficient conditions for a list of $n$ complex numbers to be the spectrum of an entry--wise nonnegative matrix of dimension $n$. This is a very difficult and long standing problem and has been solved only for $n\leq 4$. In this paper, the NIEP for a particular class of nonnegative matrices, namely Leslie matrices, is considered. Leslie matrices are nonnegative matrices, with a special zero--pattern, arising in the Leslie model, one of the best known and widely used models to describe the growth of populations. The lists of nonzero complex numbers that are subsets of the spectra of Leslie matrices are fully characterized. Moreover, the minimal dimension of a Leslie matrix having a given list of three numbers among its spectrum is provided. This result is partially extended to the case of lists of $n > 2$ real numbers.

ACS Style

Luca Benvenuti. The inverse eigenvalue problem for Leslie matrices. The Electronic Journal of Linear Algebra 2019, 35, 319 -330.

AMA Style

Luca Benvenuti. The inverse eigenvalue problem for Leslie matrices. The Electronic Journal of Linear Algebra. 2019; 35 (1):319-330.

Chicago/Turabian Style

Luca Benvenuti. 2019. "The inverse eigenvalue problem for Leslie matrices." The Electronic Journal of Linear Algebra 35, no. 1: 319-330.

Journal article
Published: 01 May 2018 in Linear Algebra and its Applications
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ACS Style

Luca Benvenuti. The NIEP for four dimensional Leslie and doubly stochastic matrices with zero trace from the coefficients of the characteristic polynomial. Linear Algebra and its Applications 2018, 544, 286 -298.

AMA Style

Luca Benvenuti. The NIEP for four dimensional Leslie and doubly stochastic matrices with zero trace from the coefficients of the characteristic polynomial. Linear Algebra and its Applications. 2018; 544 ():286-298.

Chicago/Turabian Style

Luca Benvenuti. 2018. "The NIEP for four dimensional Leslie and doubly stochastic matrices with zero trace from the coefficients of the characteristic polynomial." Linear Algebra and its Applications 544, no. : 286-298.

Chapter
Published: 06 April 2018 in Handbook of Parallel Constraint Reasoning
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Model checking has reached a maturity level that allows its techniques to be applied to the verification of industrial systems. Several algorithms and methods have been proposed to increase its effectiveness to tackle models of increasing complexity. In this chapter we present an application of Parallel Satisfiability Solving to the verification of embedded control systems. The adopted toolchain is part of the Formal Specs Verifier framework for the formal verification of Simulink/Stateflow models. The experiments we performed show that the use of a parallel satisfiability solver allows for an average speedup of an order of magnitude or more on industrial strength models.

ACS Style

Orlando Ferrante; Alberto Ferrari; Christos Sofronis; Leonardo Mangeruca; Luca Benvenuti. An Application of Parallel Satisfiability Solving to the Verification of Complex Embedded Systems. Handbook of Parallel Constraint Reasoning 2018, 617 -632.

AMA Style

Orlando Ferrante, Alberto Ferrari, Christos Sofronis, Leonardo Mangeruca, Luca Benvenuti. An Application of Parallel Satisfiability Solving to the Verification of Complex Embedded Systems. Handbook of Parallel Constraint Reasoning. 2018; ():617-632.

Chicago/Turabian Style

Orlando Ferrante; Alberto Ferrari; Christos Sofronis; Leonardo Mangeruca; Luca Benvenuti. 2018. "An Application of Parallel Satisfiability Solving to the Verification of Complex Embedded Systems." Handbook of Parallel Constraint Reasoning , no. : 617-632.

Journal article
Published: 01 December 2017 in Linear Algebra and its Applications
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ACS Style

Luca Benvenuti; Lorenzo Farina. Revisiting the linear recursions with nonnegative coefficients problem. Linear Algebra and its Applications 2017, 535, 191 -194.

AMA Style

Luca Benvenuti, Lorenzo Farina. Revisiting the linear recursions with nonnegative coefficients problem. Linear Algebra and its Applications. 2017; 535 ():191-194.

Chicago/Turabian Style

Luca Benvenuti; Lorenzo Farina. 2017. "Revisiting the linear recursions with nonnegative coefficients problem." Linear Algebra and its Applications 535, no. : 191-194.

Journal article
Published: 01 August 2016 in Journal of Cleaner Production
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Food consumption patterns and lifestyles heavily affect the environmental sustainability of food production at least in terms of water consumption and greenhouse gases emission. In this paper, a systematic procedure based on an operation research approach is presented in order to define menus with low environmental impact. The procedure optimally allocates pre-specified recipes over the three courses of twenty lunches in a month. This approach is completely new in this field since it provides directly a realistic menu. The capabilities of the proposed method are proved through the planning of two monthly schedules for a school lunch menu requiring either a minimal consumption of water or a minimal emission of greenhouse gases. They provide varied and attractive menus for children over a given set of Mediterranean cuisine recipes, ensure a proper amount of energy and nutrients intake, and have an environmental impact significantly lower than menus usually defined by nutritionists via common sense heuristic. The proposed procedure is easy to implement, has no additional cost, and is scalable, that is the set of recipes can be easily updated without changing the overall model. The results appear to be encouraging so that it would be interesting to apply the proposed procedure to some other food service areas such as company service canteens, chain restaurants or other individual establishments.

ACS Style

Luca Benvenuti; Alberto De Santis; Fabio Santesarti; Luigino Tocca. An optimal plan for food consumption with minimal environmental impact: the case of school lunch menus. Journal of Cleaner Production 2016, 129, 704 -713.

AMA Style

Luca Benvenuti, Alberto De Santis, Fabio Santesarti, Luigino Tocca. An optimal plan for food consumption with minimal environmental impact: the case of school lunch menus. Journal of Cleaner Production. 2016; 129 ():704-713.

Chicago/Turabian Style

Luca Benvenuti; Alberto De Santis; Fabio Santesarti; Luigino Tocca. 2016. "An optimal plan for food consumption with minimal environmental impact: the case of school lunch menus." Journal of Cleaner Production 129, no. : 704-713.

Journal article
Published: 08 February 2015 in The Electronic Journal of Linear Algebra
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Some results on the location of the eigenvalues of trace zero doubly stochastic matrices are provided. A result similar to that provided in [H. Perfect and L. Mirsky. Spectral properties of doubly–stochastic matrices. Monatshefte fur Mathematik, 69(1):35–57, 1965.] for doubly stochastic matrices is given.

ACS Style

Luca Benvenuti. A Note on Eigenvalues Location for Trace Zero Doubly Stochastic Matrices. The Electronic Journal of Linear Algebra 2015, 30, 599 -604.

AMA Style

Luca Benvenuti. A Note on Eigenvalues Location for Trace Zero Doubly Stochastic Matrices. The Electronic Journal of Linear Algebra. 2015; 30 (1):599-604.

Chicago/Turabian Style

Luca Benvenuti. 2015. "A Note on Eigenvalues Location for Trace Zero Doubly Stochastic Matrices." The Electronic Journal of Linear Algebra 30, no. 1: 599-604.

Preprint
Published: 01 January 2015
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In queste dispense sono raccolte le lezioni del corso di Modelli dinamici per l’Ingegneria Gestionale che si sono tenute nel corso di Laurea Magistrale in Ingegneria Gestionale dell'Università di Roma, Sapienza, dall'a.a. 2010/2011 fino all'a.a. 2014/2015. Il corso è diviso in due parti. Nella prima parte si studiano le proprieta' dei sistemi lineari positivi, e cioe' di quei sistemi di equazioni differenziali nei quali le variabili di interesse sono positive perche' rappresentano della quantita' di risorsa. Nei vari paragrafi si mostra come la sola proprieta' di positivita' ha molte implicazioni nella modellistica. Nella seconda parte vengono presentati e studiati degli esempi di sistemi non lineari con applicazioni economico/gestionali.

ACS Style

Lorenzo Farina; Luca Benvenuti. Modelli dinamici per l'ingegneria gestionale. 2015, 1 .

AMA Style

Lorenzo Farina, Luca Benvenuti. Modelli dinamici per l'ingegneria gestionale. . 2015; ():1.

Chicago/Turabian Style

Lorenzo Farina; Luca Benvenuti. 2015. "Modelli dinamici per l'ingegneria gestionale." , no. : 1.

Journal article
Published: 01 March 2014 in Linear Algebra and its Applications
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ACS Style

Luca Benvenuti. A geometrical representation of the spectra of four dimensional nonnegative matrices. Linear Algebra and its Applications 2014, 445, 162 -180.

AMA Style

Luca Benvenuti. A geometrical representation of the spectra of four dimensional nonnegative matrices. Linear Algebra and its Applications. 2014; 445 ():162-180.

Chicago/Turabian Style

Luca Benvenuti. 2014. "A geometrical representation of the spectra of four dimensional nonnegative matrices." Linear Algebra and its Applications 445, no. : 162-180.

Journal article
Published: 01 April 2013 in Automatica
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A design methodology is presented for dynamical observers of hybrid systems with linear continuous-time dynamics that reconstructs the complete state (discrete location and continuous state) from the knowledge of the inputs and outputs of a hybrid plant. We then present the application of the theory to the problem of on-line identification of the actual engaged gear for a car. The performance of the observer was tested with experimental data obtained in a Magneti Marelli Powertrain using an Opel Astra equipped with a Diesel engine. (C) 2013 Elsevier Ltd. All rights reserved

ACS Style

Andrea Balluchi; Luca Benvenuti; Maria Domenica DI Benedetto; Alberto Sangiovanni-Vincentelli. The design of dynamical observers for hybrid systems: Theory and application to an automotive control problem. Automatica 2013, 49, 915 -925.

AMA Style

Andrea Balluchi, Luca Benvenuti, Maria Domenica DI Benedetto, Alberto Sangiovanni-Vincentelli. The design of dynamical observers for hybrid systems: Theory and application to an automotive control problem. Automatica. 2013; 49 (4):915-925.

Chicago/Turabian Style

Andrea Balluchi; Luca Benvenuti; Maria Domenica DI Benedetto; Alberto Sangiovanni-Vincentelli. 2013. "The design of dynamical observers for hybrid systems: Theory and application to an automotive control problem." Automatica 49, no. 4: 915-925.

Journal article
Published: 11 October 2012 in International Journal of Robust and Nonlinear Control
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In many applicative fields, there is the need to model and design complex systems having a mixed discrete and continuous behavior that cannot be characterized faithfully using either discrete or continuous models only. Such systems consist of a discrete control part that operates in a continuous environment and are named hybrid systems because of their mixed nature. Unfortunately, most of the verification problems for hybrid systems, like reachability analysis, turn out to be undecidable. Because of this, many approximation techniques and tools to estimate the reachable set have been proposed in the literature. However, most of the tools are unable to handle nonlinear dynamics and constraints and have restrictive licenses. To overcome these limitations, we recently proposed an open‐source framework for hybrid system verification, called Ariadne, which exploits approximation techniques based on the theory of computable analysis for implementing formal verification algorithms. In this paper, we will show how the approximation capabilities of Ariadne can be used to verify complex hybrid systems, adopting an assume–guarantee reasoning approach. Copyright © 2012 John Wiley & Sons, Ltd.

ACS Style

Luca Benvenuti; Davide Bresolin; Pieter Collins; Alberto Ferrari; Luca Geretti; Tiziano Villa. Assume-guarantee verification of nonlinear hybrid systems with Ariadne. International Journal of Robust and Nonlinear Control 2012, 24, 699 -724.

AMA Style

Luca Benvenuti, Davide Bresolin, Pieter Collins, Alberto Ferrari, Luca Geretti, Tiziano Villa. Assume-guarantee verification of nonlinear hybrid systems with Ariadne. International Journal of Robust and Nonlinear Control. 2012; 24 (4):699-724.

Chicago/Turabian Style

Luca Benvenuti; Davide Bresolin; Pieter Collins; Alberto Ferrari; Luca Geretti; Tiziano Villa. 2012. "Assume-guarantee verification of nonlinear hybrid systems with Ariadne." International Journal of Robust and Nonlinear Control 24, no. 4: 699-724.

Journal article
Published: 08 August 2012 in IEEE Transactions on Automatic Control
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A standard result of linear-system theory states that a single-input-single-output (SISO) rational n th-order transfer function always has a state-space realization of the same order. In some applications, one is interested in having a realization with nonnegative entries (i.e., a positive system) and it is known that such constraints may lead to a minimal order positive realization of order much greater than the transfer function order n. In this technical note, necessary and sufficient conditions for a third-order transfer function with distinct real poles to have a third-order positive realization are given: these conditions are expressed in terms of lower bounds for the first three samples of the impulse response and therefore are very easy to check. This result is an extension of a previous result for transfer functions with distinct real positive poles.

ACS Style

Luca Benvenuti. Minimal Positive Realizations of Transfer Functions With Real Poles. IEEE Transactions on Automatic Control 2012, 58, 1013 -1017.

AMA Style

Luca Benvenuti. Minimal Positive Realizations of Transfer Functions With Real Poles. IEEE Transactions on Automatic Control. 2012; 58 (4):1013-1017.

Chicago/Turabian Style

Luca Benvenuti. 2012. "Minimal Positive Realizations of Transfer Functions With Real Poles." IEEE Transactions on Automatic Control 58, no. 4: 1013-1017.

Conference paper
Published: 01 January 2012 in Transactions on Petri Nets and Other Models of Concurrency XV
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When designing embedded systems, often the need arises to model systems having a mixed discrete and continuous behavior. Such hybrid systems commonly consist of a discrete control part that operates in a continuous environment and may be represented by hybrid automata. We recently proposed an open-source framework for hybrid automata analysis, called Ariadne, which exploits approximation techniques based on the theory of computable analysis. In this paper we will show how the approximation capabilities of Ariadne can be used to verify nonlinear hybrid automata inside a design space by means of reachability analysis. In particular, we will use the tool to solve a problem of dominance checking.

ACS Style

Luca Benvenuti; Davide Bresolin; Pieter Collins; Alberto Ferrari; Luca Geretti; Tiziano Villa. Ariadne: Dominance Checking of Nonlinear Hybrid Automata Using Reachability Analysis. Transactions on Petri Nets and Other Models of Concurrency XV 2012, 79 -91.

AMA Style

Luca Benvenuti, Davide Bresolin, Pieter Collins, Alberto Ferrari, Luca Geretti, Tiziano Villa. Ariadne: Dominance Checking of Nonlinear Hybrid Automata Using Reachability Analysis. Transactions on Petri Nets and Other Models of Concurrency XV. 2012; ():79-91.

Chicago/Turabian Style

Luca Benvenuti; Davide Bresolin; Pieter Collins; Alberto Ferrari; Luca Geretti; Tiziano Villa. 2012. "Ariadne: Dominance Checking of Nonlinear Hybrid Automata Using Reachability Analysis." Transactions on Petri Nets and Other Models of Concurrency XV , no. : 79-91.