Sliding Mode Secure Control for Markov Jump Systems: Dealing With Random Nonuniform Sampling Issues

This article investigates the sliding mode control (SMC) problem for a class of Markov jump systems (MJSs), in which the system states are sampled randomly and nonuniformly according to Markov chain. Besides, the transmission of sampled states through the shared network channel is inevitably subject to deception attacks obeying Markov model. In order to facilitate the subsequent design and analysis, the encountered three Markov chains are first mapped into one, meanwhile, a suitable mode detection scheme is put forward to simultaneously detect the partially inaccessible modes including the controlled system modes and attack modes. And then, a detected-mode-dependent sliding mode controller is designed to effectively cope with the stochastic features of sampling processes and attack occurrences. Furthermore, the reachability of the specified sliding surface and the mean-square exponential ultimate boundedness of the closed-loop system are analyzed and the corresponding conditions are derived. Finally, two simulation examples are provided to illustrate the designed control method.