The Robust Passive Control For Uncertainty Linear Time-varying Delay Systems

Uncertainty and time-delay generally exist in practical systems. In practical systems, uncertainties may appear because of measurement error, change of the input condition, sensor and other devices abnormal operating and the disturbance from outside. As the existing of the uncertainties, the analysis and design of systems and the practical research will be more difficult. So the research of the uncertain time delay systems is always one of the most difficult and hottest problems in the research of control theory. The theory of dissipative property is important in the stability research of time delay systems. Passive control is a special case of dissipative control, which is generally concerned in recent years. In the paper, the robust passive control problem of polytopic uncertain time varying systems with time delay is discussed by use of Lyapunov stability theory and the method of linear matrix inequalities, based on the work of predecessors, we do researches and have the corresponding result as follows:The problem of robust passive control of polytopic uncertain linear time varying systems with time delay based on state feedback is discussed. By constructing Lyapunov-Krasovskii functional, the sufficient condition of asymptotic stable and strict passive of systems is given, and then the sufficient condition of strong robust stable and strict passive of systems is also obtained. According to the condition of the robust passivity of the system, the robust passive controller is designed on the basis of memoryless/memory linear state feedback. The problem of robust passive control of polytopic uncertain linear time varying systems with time delay based on dynamic output feedback is discussed. By using of the result of the relation between nuclear space of matrix and matrix inequalities the sufficient condition of the system existing dynamic output feedback controller is obtained in algebra and combining the elimination method, the dynamic output feedback passive controller is designed, and the implement steps of passive controller is also given. The problem of robust passive control of polytopic uncertain linear time varying systems with time delay based on observer state feedback is discussed. An observer state feedback controller is designed, by constructing Lyapunov-Krasovskii functional, the sufficient condition of robust passive of the closed loop system is given out, and then the method of designing the controllers for the polytopic uncertainties is acquired, also the controller can be constructed by the solution of the linear matrix inequalities.The results in the paper are given in the form of linear matrix inequalities, so they can be solved by Matlab software easily, the corresponding numeric examples verify the feasibility and the validity of the method.