Adaptive sliding mode control of Markov jump systems with completely unknown mode information

This paper aims to investigate the problem of adaptive sliding mode control for Markov jump systems with deficient transition probability. Different from the existing literature, we propose a novel method to design a mode-dependent sliding mode controller when the mode information is completely unknown, while the controller gain parameters can be designed by solving feasible conditions. Firstly, by designing an integral-type sliding surface, on which an ideal sliding mode dynamics is obtained. Then, for different types of mode transition information, a set of feasible easy-checking stochastic stability criteria are proposed for the sliding mode dynamics in terms of strict linear matrix inequalities. Further, relying on the parameters obtained from the stability criteria, an adaptive sliding mode controller is successfully designed with respect to different types of system mode transition information. Finally, a numerical example is provided to illustrate the advantage of the developed strategy.