The Analysis And Synthesis Of Stability In Several Delay Systems

In the second chapter of this paper, the instability of time-varying systems with multi-delay is discussed by using the comparison principle and vector Lyapunov function. In§2.1, a class of linear time-varying continual systems with multi-delay is studied first for its instability. By constructing the linear constant assisted system with multi-delay, applying corresponding comparison principle and vector Lyapunov function, the sufficiency theorem of instability for linear time-varying continual system with multi-delay are obtained. And then, the instability of both a class of nonlinear and interval coefficient time-varying continual systems with multi-delay is studied, and the theorems of instability in above systems are obtained. In§2.2, the instability of a class of linear time-varying discrete systems with multiple non-integral delays is discussed, and then the instability of both a class of nonlinear and interval coefficient linear time-varying discrete systems with multiple non-integral delays. By using the comparison principle of discrete system with time-delay and vector Lyapunov function, some sufficiency theorems of instability for these systems are obtained. Final, an example is given to demonstrate the feasibility of the obtained results.In the third chapter, the Lyapunov's method is employed to study the asymptotic stability and the problem of stabilization on the singular systems with time-delay. Firstly, a type of Lyapunov equation is presented to solve the asymptotic stability of singular systems with time-delay; the theorem of asymptotic stability is obtained. Then, controller with time-delay and controller without time-delay of singular control systems with time-delay are studied. By using the corresponding Riccati equation, the state feedback law is designed, and the sufficiency theorems of above control systems are obtained. Final, an example shows that the theorems of this chapter are feasible.