Studies On Stability And Control Problem Of Singular Linear Systems Under Impulsive Or Switched Mechanism

A singular system is a dynamical system which is able to describe both static and dynamic constraints at the same time. Singular system is widely used in the fields of power systems, economic systems, and electronic networks. On the other hand, impulsive and switch process widespread in many practical system models. Singular system under impulsive or switched mechanism can describe the evolution of complex systems more deeply and has more challenging in theory study. In this dissertation, the effects of impulsive and switched mechanism on the stability and closed-loop performance of the system are studied in this dissertation. On this basis, the dissertation discusses the design method of optimal controller. The main work are as follows:(1) The problem of H∞ control for linear singular time delay system subject to impulsive perturbations has been studied. With the aid of impulse-time-dependent Lyapunov functionals and the use of differential inequality, we get a sufficient stability condition for stability and finite L2 gain performance. The design criterion of the H∞ state feedback controller is given in the finally.(2) The exponential stability of a class of linear switched singular systems has been studied. As for inconsistent initial conditions, a refined description of state jumps of the switched singular system is formulated. By utilizing the time-varying Lyapunov function, convex combination technique and combing with the linear matrix inequality approach, we get a sufficient condition for the exponential stability of the switched singular system with stable subsystems.(3) The stability and stabilization of linear neutral delay system with impulsive action has been studied. Considering the characteristics of neutral-type system, we introduce a new model transformation. Thus the techniques for stability analysis of switched normal systems can be applied to neutral-type system directly. In the framework of impulsive singular time delay systems, the quantitative relation between the impulsive and the exponential stability of the system is constructed. On this basis, the design criteria of the continuous state feedback controller and impulsive state feedback controller are established.