H‐infinity fault‐tolerant control for Markov jump system with actuator time delay

Abstract

Abstract This study investigates H‐infinity fault‐tolerant control for Markov jump systems with actuator time delay. The main objective is to obtain some theorems such that the corresponding Markov jump systems with actuator time delay to be H‐infinity stable and with some fault‐tolerant performances. First, based on an integral transformation, the Markov jump systems with actuator time delay are described in a system description with a distributed time‐delay item. Second, based on utilizing the linear matrix inequality theory, a positive energy functional, which includes a double integral item, is constructed. Then, after some mathematical operations, a sufficient condition is obtained for the Markov jump systems with actuator time delay to be H‐infinity stable. If the condition is solvable, fault‐tolerant controller can be gotten to guarantee the controlled system to be H‐infinity stable no matter there are some actuator faults existing in the system or not. Finally, examples are given to show the usefulness of the obtained theorem.