Hybrid asynchronous sliding mode control for hidden Markovian jump systems under optimized design

Abstract

This article is concerned with the hybrid design of transition rates and asynchronous sliding mode control (SMC) law for continuous‐time Markovian jump systems with matched disturbances. First, a sufficient condition is established to ensure the stochastic ultimate boundedness (SUB) of the unforced systems, which are driven only by using the designed stabilizing transition rates. Furthermore, by considering the system modes are unavailable for the controller, a hidden Markov mode detector is introduced to emit the detection modes. Based on the mode detection probabilities, a hybrid design approach is proposed by co‐designing of transition rates and asynchronous SMC law, which ensures the SUB and disturbance attenuation performance of the resulted closed‐loop systems. The obtained sufficient conditions are solved via two iterative optimization algorithms, which combine cone complementarity linearization and genetic algorithm. Finally, a numerical example with three comparison cases is provided to illustrate the proposed results.