The Study Of Stability And Stabilization For Neutral Systems With Time Delays

Time delays are frequently encountered in various engineering systems, and the existence of time delays may result in instability, oscillation and poor performance of a system. Neutral delay system contains delays both in its states and in the derivatives of its state. It can be found in such places as population ecology, distributed networks containing lossless transmission lines, heat exchangers, electric networks, etc. In this thesis, the problems of stability and stabilization for several classes uncertain neutral systems are investigated. In the first chapter, the development of delay systems, some descriptions of the primary methods that authors always use and the primary research methods and current research status on stability of neutral delay systems are introduced. In the second chapter, the problems of exponential stability and robust stabilization for neutral delay system with variable delays under two different initial state spaces are investigated. The delay-independent sufficient conditions for exponential stability and the existence of memoryless state feedback controller are derived in terms of linear matrix inequalities by using the Razumikhin-Lyapunov technique. In the third chapter, the problems of robust stability and stabilization for uncertain neutral systems with distributed delay are investigated. The delay-dependent sufficient conditions for robust stability and the existence of memoryless state feedback controller are derived in terms of linear matrix inequalities by using Fridman's singular system method. In the fourth chapter, the problems of the robust stability and stabilization for uncertain neutral systems with state and input delays are investigated. The delay-dependent sufficient conditions for robust stability and the existence of memoryless state feedback controller are derived in terms of linear matrix inequalities by using Fridman's singular system method.