The Stability And Control For A Class Of Neutral System With Time Delay

The study of the time-delay systems of neutral type became a hotspot and had attracted more and more researchers. These systems contain not only information of the past state but also information of the derivative of the past state. These systems can be depicted by the differential function of neutral typy. The study of the neutral systems will offer better theoretical basic and means for dealing with practice.In this paper studied stability and control problems of the neutral time-delay systems based on linear matrix inequalities theory and by using the descriptor model.The stability criterion and strictly dissipative controller,H_∞guaranteed cost controller of the neutral time-delay systems were given. The main work as following:Firstly, the problem of strictly dissipative state feedback control for neutral systems with time-delay is studied. The neutral system is equivalently represented as a descriptor system, then a sufficient condition is presented for existence of the dissipative controller, and a illustrative example is given to demonstrate the effectiveness of the design method.Secondly, a strictly dissipative state feedback controller design is considered for a class of uncertain neutral systems with time-delay. A condition for the existence of strictly dissipative state feedback control law is derived on the basis of Lyapunov stability theory and linear matrix inequalities method, and then an example is given to demonstrate the efficiency of the proposed approach.Thirdly, a robust state feedback controller design is considered for a class of time-delay neutral system with nonlinear uncertainty. The problem of robust H_∞control is studied. Based on Lyapunov stability theory and linear matrix inequality theory, a sufficient condition is presented for existence of the controller. By solving a linear matrix inequality, the state feedback controller is obtained.In the end, the problem of delay-dependent robust H_∞guaranteed cost control for a class of uncertain neutral type descriptor system with time-varying delays is studied. A new sufficient condition of H_∞robust stabilization and satisfies guaranteed cost index is given for the systems by constructing Lyapunov function, linear matrix inequalities approach and descriptor system approach,then an example is given to validate the result.