The Analysis And Application Of Stability For Several Types Of Delay Differential Systems

Time delays are frequent in the real world, they are main source of performance degradation and instability in many dynamic systems. Thus, it is a great importance to study the stability analysis for the time-delay systems. Many control systems have delay not only in the state but also in the state derivative, they are called neutral systems. The singular system model is a natural presentation of dynamic systems and can describe a larger class of systems than regular ones. Stabilization is the premise of practical systems normal operation and the stabilization is a significant issue for systems control theory. So it is essential that analysis the stability of systems with time delay.This paper has four chapters, which mainly discusses the sliding mode control or stability problem for several class of differential systems.Chapter1Some background knowledge of singular delay system, neutral system and uncertain system are introduced, and the work what the paper done is given.Chapter2We discuss the sliding mode control for a class of uncertainty singular delayed systems with external perturbation. By decomposing the uncertainty singular systems with multiple delays into two subsystems, first the switching function is designed, sufficient condition of asymptotic stabilization of the sliding mode motion expressed in terms of linear matrix inequalities is established.Chapter3All-delays stability analysis for singular delayed systems with distributed delays is studied. We can get the sufficient and necessary condition of the all delays stability of the system. Also we generalize the main result to the system that has several delays.Chapter4The asymptotic stability of linear neutral differential system with double delays is investigated. By constructing matrices, the simple delay-independent Hurwitz stability criteria are derived. The conclusions are drawn based on the spectral radius of modulus matrices which makes the validation easier.