Improved passivity‐based control for Markovian jump singular systems with aperiodic sampling and actuator failures

Abstract

This aricle investigates the passivity‐based control problem for Markovian jump singular systems with aperiodic sampling and actuator failures. Firstly, in order to fully consider the system information, two novel mode‐dependent Lyapunov–Krasovskii functions (LKFs) are constructed, which are composed of one‐sided and two‐sided looped‐functionals respectively. Based on these two LKFs and an improved integral inequality, two stochastic admissibility and robust passivity criteria with lesser conservatism are given by using linear matrix inequalities (LMIs). Moreover, through these theorems, it is proved that the positive constraint of LKFs can be relaxed from all times to sampling times for Markovian jump singular systems with aperiodic sampling and actuator failures. Then, two aperiodic sampled‐data controller algorithms are proposed by LMIs to ensure the stability of the systems. Finally, A numerical example and a model of DC motor driving an inverted pendulum are provided to demonstrate the validity of the main results.