The Research Of Stability For Time-delay Differential Systems

Time delays frequently appear in many practical systems, they are regarded as the major source of instability and poor performance. Therefore, a great amount of effort has been devoted to the stability analysis for the time-delay systems. There are many control systems having delay not only in the state but also in the state derivative, such systems are called neutral systems. Recently, there has been rapidly growing interest in the problem of the stability analysis for neutral delayed systems. The singular system model is a natural presentation of dynamic systems and can describe a larger class of systems than regular ones. Over the past decades, much attention has been focused on stability analysis for singular linear systems with time delay. Fractional differential equations are introduced in order to describe and imitate the practical phenomena more exactly. Thus there are much theoretical value and practical meaning of the research on fractional differential equations and systems.In this paper, we are concerned with the robust stability problem for several class of differential systems. And a sliding mode control design for fractional systems is also given in it. There are four chapters in this paper.In chapter1, some background knowledge of neutral differential system, singular system and fractional differential system are introduced, and the preliminary knowledge which is necessary in the paper is given.In chapter2, we discuss the robust stability criteria for a class of neutral uncertain-ty delayed systems with nonlinear perturbation. Based on the augmented Lyapunov-Krasovskii functional and the free-weighting matrix method, sufficient conditions of delay-dependent stability expressed in terms of linear matrix inequalities are obtained.In chapter3, the dependent-delay stability analysis for singular linear systems with multiple delays is studied. By decomposing the singular linear systems with multiple de-lays into slow and fast subsystems, LMI-based delay-dependent stability and stabilisation conditions are established.In chapter4, we deal with a sliding mode control design for a class of linear fractional systems with state delay, and the existence of the sliding mode and the stability of the proposed control design are discussed.