Stability And Control Of The Discrete Singular Systems With Time-Delay

Singular systems, also called general systems,implicit systems, differential algebraic systems. It is composed by the slowly varying dynamic layer subsystem described by differential (difference) equations and the fast changing static layer subsystems described by algebraic equations, is the non-mathematical model large-scale systems combined by the traditional static and dynamic system, which has multi-layer, multi-level, multi-objective, large-scale, complex features. Singular systems with time-delay, discribed by the generalized differential (difference) equation or functional differential equations, and generated in the actual model, such as motor, measuring the economy's inputs and outputs, the environment and spacecraft attitude. Since hysteresis is the common phenomena and problems in objective world and engineering, but also due to the recent rapid development of computer technology, discrete singular systems with time delay caused by re-engineering, control, and the scientific community's particular attention. In this paper, we discuss the stability of discrete time-delay singular systems,and variable structure control for a kind of discrete systems with time-varing delay. The main contents include the following components:The first chapter introduces the history and development of the singular system.The second chapter discusses the general solution of the discrete (delay) sigular system, the local reachability and local controllability of the basic concepts, and by using Z-transform, a new solution expression is got for the discrete systems with delay or without delay, and a new necessary and sufficient condition is obtained about the systems'local reachability and local controllability. Meanwhile, a numerical example are given to shows the effectiveness and feasibility of the result. In the third chapter, the stability is discussed for the discrete singular systems with time-delay. And the stability criteria of the dicrete singular systems with multiple time-varying delays is given.In the chapter forth, for a class of discrete systems with time-varying delay, by using Lyapunov theory and LMI theory, the variable structure controller are designed based on the state observer in case of unknown system state.