In this paper we deal with the finite-time stability problem for quadratic systems. Such class of systems plays an important role in the modeling of a wide class of nonlinear processes (electrical, robotic, biological, etc.). The main results of the paper consist of two sufficient conditions for finite-time stability analysis and finite-time stabilization via static state feedback; both conditions are given in terms of the feasibility of a convex optimization problem, involving linear matrix inequalities. A numerical example illustrates the applicability of the proposed technique.

Mechanistic-based Model simulations (MM) are an effective approach commonly employed, for research and learning purposes, to better investigate and understand the inherent behavior of biological systems. Recent advancements in modern technologies and the large availability of omics data allowed the application of Machine Learning (ML) techniques to different research fields, including systems biology. However, the availability of information regarding the analyzed biological context, sufficient experimental data, as well as the degree of computational complexity, represent some of the issues that both MMs and ML techniques could present individually. For this reason, recently, several studies suggest overcoming or significantly reducing these drawbacks by combining the above-mentioned two methods. In the wake of the growing interest in this hybrid analysis approach, with the present review, we want to systematically investigate the studies available in the scientific literature in which both MMs and ML have been combined to explain biological processes at genomics, proteomics, and metabolomics levels, or the behavior of entire cellular populations. Elsevier Scopus®, Clarivate Web of Science™ and National Library of Medicine PubMed® databases were enquired using the queries reported in Table 1, resulting in 350 scientific articles. Only 14 of the 350 documents returned by the comprehensive search conducted on the three major online databases met our search criteria, i.e. present a hybrid approach consisting of the synergistic combination of MMs and ML to treat a particular aspect of systems biology. Despite the recent interest in this methodology, from a careful analysis of the selected papers, it emerged how examples of integration between MMs and ML are already present in systems biology, highlighting the great potential of this hybrid approach to both at micro and macro biological scales.

This paper deals with the problem of stabilizing a bilinear system via linear state-feedback control. The proposed procedures enable us to compute a static state-feedback controller such that the zero-equilibrium point of the closed-loop system is asymptotically stable; moreover, it ensure that an assigned polytopic region is enclosed into the domain of attraction of the equilibrium point. The controller design requires the solution of a convex optimization problem involving linear matrix inequalities. The applicability of the technique is illustrated through an example, dealing with the design of a controller for a Cuk dc-dc converter.