Non‐fragile reliable guaranteed cost control and L₂‐gain analysis for saturated switched nonlinear systems

Abstract

For the nonlinear continuous‐time saturated switched system, this article investigates the problem of non‐fragile reliable guaranteed cost control of the system. Due to the simultaneous occurrence of controller perturbation, actuator saturation and actuator failure, when designing the cost function, this article considers three scenarios affecting the system performance, controller perturbation, actuator saturation and actuator failure, simultaneously in the cost function, which has not been investigated in the existing literature. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization of non‐fragile reliable guaranteed cost control and the performance index. In order to ensure the exponential stabilization of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and the non‐fragile reliable guaranteed cost state feedback controllers are designed by using the minimum dwell‐time method. Furthermore, by solving optimization problems with linear matrix inequality constraints, the minimum upper bound of the cost function and the performance of the system are determined. At the end of the article, we give a numerical example to verify the effectiveness of the proposed approach.