Uncertain Linear Descriptor Systems Research Articles

Admissibility analysis of discrete linear time-varying descriptor systems

This paper deals with the problem of admissibility analysis (i.e. regularity, causality and exponential stability) of discrete-time linear descriptor systems with uncertain time-varying parameters in the system state-space model matrices. The parameters enter affinely into all the matrices, and both their admissible values and variations are assumed to belong to given intervals. First, necessary and sufficient admissibility conditions for uncertainty-free discrete linear time-varying descriptor systems are presented. Next, strict linear matrix inequality conditions based on parameter-dependent Lyapunov functions are proposed to ensure robust admissibility of uncertain linear descriptor systems. Both the cases of Lyapunov functions with affine and quadratic dependence on the system uncertain parameters are considered. The robust admissibility analysis methods incorporate information on available bounds on both the admissible values and variation of the uncertain parameters. Numerical examples are presented to demonstrate the potentials of the proposed methods.

Robust<tex>$H_infty$</tex>Filter Design of Uncertain Descriptor Systems with Discrete and Distributed Delays

The robust H/sub /spl infin// filtering problem for a class of continuous-time uncertain linear descriptor systems with time-varying discrete and distributed delays is investigated. The time delays are assumed to be constant and known. The uncertainties under consideration are norm-bounded, and possible time-varying, uncertainties. Sufficient condition for the existence of an H/sub /spl infin// filter is expressed in terms of strict linear matrix inequalities (LMIs). Instead of using decomposition technique, a unified form of LMIs is proposed to show the exponential stability of the augmented systems. The condition for assuring the stability of the fast subsystem is implied from the unified form of LMIs, which is shown to be less conservative than the characteristic equation based conditions or matrix norm-based conditions. The suitable filter is derived through a convex optimization problem. A numerical example is given to show the effectiveness of the method.

Robust controllability and robust closed-loop stability with static output feedback for a class of uncertain descriptor systems

This paper considers robust controllability for uncertain linear descriptor systems with structured perturbations. Necessary and sufficient conditions based on the μ-analysis are obtained by transforming the problem into checking the nonsingularity of a class of uncertain matrices. Also a tight bound is obtained in terms of μ for keeping the closed-loop system regular, impulse-free and stable under a preconstructed static output feedback. An example is given to illustrate the results.

On the stability of uncertain linear descriptor systems

Lyapunov stability theory for conventional systems is extended in a natural way to a class of uncertain descriptor (singular) systems with or without control. It is shown that the resulting stability can be determined via the solution of a generalized algebraic Riccati matrix equation. We first investigate the response upper bound and stability for the perturbed open-loop system, and then construct two types of robust stabilizers for systems possessing the properties of impulse controllability or normalizability.

Necessary and sufficient conditions for the controllability of linear interval descriptor systems

In this paper, we investigate a class of uncertain linear descriptor systems with interval plants, and give necessary and//or sufficient conditions for controllability. Examples are also given to illustrate the results. The corresponding results for the dual observability robustness problems are straightforward extensions.