| Abstract: Stability is the premise of normal work for practical systems. Stability analysis and synthesis of systems is an important subjuct in control theory. A necessary and sufficient condition on stability for discrete-time singular systems is given mainly by applying special restricted systems equivalent transformations and an appropriate generalized Lyapunov equation.Robustness of uncertain systems means that, under the condition of some uncertainties, the stability, asymptotical regulation and dynamic features can be retained, i.e., these systems can resist uncertainties. The H_ ∞control theory for systems has been investigated well in robust control theory. Basing on linear matrix inequality, this paper investigates an equivalent condition on proportional and derivative state feedback stabilization for a class of uncertain singular systems, proportional and derivative state H_ ∞ control, H_ ∞ performence analysis of uncertain nonlinear systems with time-varying delay, state feedback H_ ∞ control and provides some algorithms for corresponding controlled systems, such that the closed-loop systems satisfy:(i) the closed-loop system is uniformly asymptotically stable(ii) the H_ ∞ norm of the transfer function from disturbances ω to the controlled output z satisfiesThis paper is divided into four chapters to discuss the above results.Chapter 1: Some mathematic models and background of systems under consideration and the target and significance of reserch on robust control are introduced. As for the H_ ∞ control for uncertain systems, we generalize the existing results in outline.Chapter 2: A necessary and sufficient condition on stability for discrete-time singular systems is given mainly by applying special restricted systems equivalent transformations and an appropriate generalized Lyapunov equation. Furthermore, by combining a criteria for impulse freedom, a new necessary and sufficient condition on stability and impulse freedom will be derived for discrete-time singular systems.
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