Reliability Of Switched Systems With Delay Control

In actual systems, actuators often suffer from failure inevitably because of many external disturbance. Classical H∞control and l2-l∞control may not provide satisfactory perfor-mance, even make the closed-loop systems not stable. Owning to the demands of systems reliability, the reliable control problem becomes more important. In this paper, we will focus on the study of the problems of the reliable H∞controller and the reliable l2-l∞controller for a class of uncertain switched linear time-delay systems.The main contributions include:1. The problem of the reliable H∞control for a class of uncertain switched linear time-delay systems with actuator failures.When actuators suffer from " serious failure ", the survived actuators can not stabilize the given systems. Based on the multiple Lyapunov function technique and by choosing an appropriate Lyapunov function, we derived sufficient conditions for the existence of state feedback reliable H∞controller in terms of linear matrix inequalities(LMIs).2. The problem of the reliable l2-l∞control for a class of uncertain switched linear time-delay systems with actuator failure.When actuators suffer from " serious failure ", the survived actuators can not stabilize the given systems. Based on average dwell time and multiple Lyapunov function technique, a sufficient condition is proposed in strict LMIs, which guarantees the existence of state feedback l2-l∞controller for the existence of state feedback l2-l∞controller in terms of linear matrix inequalities (LMIs).3. The problem of the reliable l2-l∞dynamic output feedback control for a class of uncertain linear systems with time delay based on a switching method.When actuators suffer from " serious failure ", the survived actuators can not stabilize the given systems, under the condition that activation time ratio between the system without actuator failures and the system with actuator failures is not less than a specified constant, the uncertain systems with time delay can be viewed as switched systems. Based on average dwell scheme, the reliable l2-l∞dynamic output feedback controllers are derived in terms of linear matrix inequalities(LMIs) such that the resulting closed-loop systems is exponentially stable.