This note presents a stability condition for timevariant uncertain discrete delay systems, where the uncertainty set is nite and constraints on the allowable sequences of system matrices are imposed. The proposed stability condition is necessary and suÆcient and can be viewed as a modi ed combination of two existing conditions for time-variant systems with polytopic uncertainties. The introduce...

In this paper, stabilizability problems for discrete and continuous time linear systems with switching or polytopic uncertainties are dealt with. Both state feedback and full-information controllers are considered, possibly with an integral action. Several cases will be analyzed, depending on the control, the uncertainty and the presence of uncertainties in the input matrix. A complete overview...

This paper presents synthesis procedures for the design of both robust and gain scheduled H∞ static output feedback controllers for discrete-time linear systems with timevarying parameters. The parameters are assumed to vary inside a polytope and have known bounds on their rate of variation. The geometric properties of the polytopic domain are exploited to derive a finite set of linear matrix i...

Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coefficients of a polynomial. An application to the design of fixed-order controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed, based on LMI optimization. The key ingredient in the design procedure resides in the choice of a...

This paper is devoted to stability analysis and synthesis of uncertain systems subject to input saturation. A new parameter-dependent Lyapunov function analyzing approach is proposed to reduce the conservatism in stability analysis for the polytopic systems subject to input saturation. Some new stability conditions and a gain-scheduling controller design method are then developed by the LMI opt...

The paper provides a survey of some recent quadratic stability methods for static output feedback robust controller design for linear continuous-time invariant systems with convex polytopic uncertainty and their mutual comparison. Robust controller design is based on linear matrix inequalities (LMIs) conditions and single Lyapunov functions. The presented quadratic stability methods are compare...

This work is further focused on analyzing a bound for a reachable set of linear uncertain systems with polytopic parameters. By means of L-K functional theory and novel inequalities, some new conditions which are expressed in the form of LMIs are derived. It should be noted that novel inequalities can improve upper bounds of Jensen inequalities, which yields less conservatism of systems. Conseq...

This paper presents new robust linear matrix inequality conditions for full order robust H∞ filter design of discrete-time polytopic linear systems affected by a timevarying delay. Thanks to the use of a larger number of slack variables, the proposed conditions are less conservative than the existing methods. Numerical experiments illustrate the better performance of the proposed filter design ...

In this paper we focus on observability for hybrid systems in the mixed-logic dynamical form. We show that the maximal set of observable states, that is usually non convex and disconnected, can be represented as the union of finitely many polytopic regions. The argument, that is based on multi-parametric programming theory, is constructive and provides an algorithm for the computation of the re...

In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As approximation space, it is applied to discontinuous Galerkin methods upwind scheme for steady-state convection-diffusion-reaction problems over polytopic meshes. The optimal error estimates are provided in both diffusion-dominated and...