This study concerns the observer design for Lipschitz non‐linear descriptor systems. It introduces a new observer structure called a generalised dynamic observer, which is more general than the proportional and proportional–integral observers. The originality of the proposed observer is that it provides additional degrees of freedom in the observer design, which can be used to increase steady‐state accuracy and to improve robustness in estimation against modelling errors. Conditions for the existence and stability of this observer are given in terms of linear matrix inequalities. Reduced‐order and full‐order observers can be designed directly by using the proposed unified approach. The effectiveness of the developed method is illustrated by two numerical examples where impulse and impulse‐free cases are considered, a comparison between the generalised dynamic observer, the proportional observer, and the proportional–integral observer is given to show the observers performances.

For this research, the properties of the logistic growth model for independent and coexisting species were used to set definitions for the possible regulation of one or two growth variables through their coupling parameters. The present analysis is done for the single-species Verhulst model without coupling, the single-species Verhulst model coupled with an exogenous signal, and the two-species Verhulst coexistence growth model which represents six different ecological regimes of interaction. The models’ parameters, such as the intrinsic growth rate and the coupling, are defined. Finally, the control results are expressed as lemmas for regulation, and they are shown using a simulation example of a fish population growing independent of human interaction (no harvesting, no fishing) and the simulation of the regulation of said population when the coupling of fish and humans is involved (harvesting, fishing).

This paper presents a new approach to $H_{\mathrm{\infty }}$ observer design for a class of nonlinear systems with unknown inputs. The considered systems are composed of a linear part perturbed by an additive Lipschitz nonlinearity in the presence of unknown inputs and disturbances. Our objective is to present a dynamical observer which generalizes the Luenberger observer, called also the Proportional Observer (PO), and the Proportional-Integral Observer (PIO). The advantages of this observer are its robustness with respect to uncertainties and modeling errors and its steady state accuracy. The presented method also unifies the reduced and the full order design. An example using a one-link-flexible joint robot is given to illustrate our approach.