Robust Stability Analysis And Control For Discrete Singular Systems With Delay

With the rapid development of the computer techniques, the subject of discrete systems has recently received much attention in the fields of engineering, control and science. This dissertation, which is made up of seven parts, focuses on the robust stability and control of discrete singular systems with delay.In section â… , the general solution, local reachability and local controllability is discussed for discrete singular systems with delay and without delay. First, by Z-transform, the general solution is derived for discrete singular systems with delay and without delay, next, necessary and sufficient conditions are established for local reachability and local controllability. At last, a numerical example is presented.Section â…¡ analyzes qualitatively and quantitatively discrete singular systems with delay and quadratic delay. Firstly, it discusses qualitatively and quantitatively discrete system with delay and quadratic delay by Lyapunov's method , and estimates the sizes of the uniform stability region and asymptotic stability region for the systems. Secondly, for a sufficiently small delay, uniform stability and asymptotic stability is obtained for discrete singular systems with the delay. Finally, an important problem of the maximum stability region is proposed.Section â…¢ investigates the stability and robust stability for discrete singular systems with multiple delays. Firstly, two asymptotic stability criteria are established for discrete singular systems with multiple delays. One is a direct test and another is a boundary test. Secondly, an simple robustness stability criterion independent of delays is derived and the effective quantitative measures is provided for robust stability and performance robustness of discrete uncertain singular systems with multiple delays.Section â…£ investigates the robustness for pole assignment of discrete uncertain singular systems with multiple delays, and presents sufficient criteria , that is all the limited poles of discrete uncertain singular systems with multiple delays lie in certain specified regions. No restriction is imposed on the shapes of the specified regions.