Jacques Bernussou

A new discrete-time robust stability condition☆

A new robust stability condition for uncertain discrete-time systems with convex polytopic uncertainty is given. It enables to check stability using parameter-dependent Lyapunov functions which are derived from LMI conditions. It is shown that this new condition provides better results than the classical quadratic stability. Besides the use of a parameter-dependent Lyapunov function, this condition exhibits a kind of decoupling between the Lyapunov and the system matrices which may be explored for control synthesis purposes. A numerical example illustrates the results.

A new robust D-stability condition for real convex polytopic uncertainty

Abstract The problem of robust D -stability analysis with respect to real convex polytopic uncertainties is tackled. A new LMI -based sufficient condition for the existence of parameter-dependent Lyapunov functions is proposed. This condition generalises previously published conditions. Numerical comparisons with quadratic stability results as well as previous results based on parameter-dependent Lyapunov functions illustrate the relevance of this new condition. Finally, this result appears to be promising for robust multi-objective performance analysis and control synthesis purposes.

Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties

Abstract In this paper, we consider discrete time systems with polytopic time varying uncertainty. We look for a class of parameter dependent Lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter. We show that extending the new discrete time stability condition proposed by de Oliveira et al. (Systems Control Lett. 36 (1999) 135.) to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a Lyapunov function. This allows to check asymptotic stability of the system under study. The obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem.

Continuous-time analysis, eigenstructure assignment, and H/sub 2/ synthesis with enhanced linear matrix inequalities (LMI) characterizations

This note describes a new framework for the analysis and synthesis of control systems, which constitutes a genuine continuous-time extension of results that are only available in discrete time. In contrast to earlier results the proposed methods involve a specific transformation on the Lyapunov variables and a reciprocal variant of the projection lemma, in addition to the classical linearizing transformations on the controller data. For a wide range of problems including robust analysis and synthesis, multichannel H/sub 2/ stateand output-feedback syntheses, the approach leads to potentially less conservative linear matrix inequality (LMI) characterizations. This comes from the fact that the technical restriction of using a single Lyapunov function is to some extent ruled out in this new approach. Moreover, the approach offers new potentials for problems that cannot be handled using earlier techniques. An important instance is the eigenstructure assignment problem blended with Lyapunov-type constraints which is given a simple and tractable formulation.

On a convex parameter space method for linear control design of uncertain systems

This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors’ knowledge, this is one of the first numerical procedures able to handle and solve this interesting design problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.

Pole assignment for uncertain systems in a specified disk by state feedback

In this paper the problem of pole assignment in a disk by output feedback for continuous-or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given.

Decentralized control through parameter space optimization

The decentralized control problem for linear dynamic systems is revisited using a parameter space approach which enables the definition of the decentralized feedbacks from the existence of non-empty parameter convex sets. The convexity property enables the derivation of efficient numerical algorithms based on standard approaches in convex programming. The continuous-time and discrete-time cases are investigated and the decentralized control design is also treated to meet other important assignments such as: optimal H2 performance index, absolute stability, H∞ prescribed attenuation and robustness against actuator failures. Some numerical experiments illustrate the potential of this new control design.

H 2 and

This paper investigates robust filtering design problems in H2 and

H_\infty

H_\infty

Robust Filtering for Discrete-Time Linear Systems

spaces for discrete-time systems subjected to parameter uncertainty which is assumed to belong to a convex bounded polyhedral domain. It is shown that, by a suitable change of variables, both design problems can be converted into convex programming problems written in terms of linear matrix inequalities (LMI). The results generalize the ones available in the literature to date in several directions. First, all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured. Then, assuming the order of the uncertain system is known, the optimal guaranteed performance H2 and