Sliding mode control of Markov jump systems: Multi-processor based observer approach

This paper investigates the implementation of a sliding mode control law with an observer-based state-feedback controller for Markov jump systems, utilizing output measurements obtained from a communication network followed by a multi-processor block. The employed Round-Robin strategy schedules node activation in communication. In this setup, hidden Markov models with specific transition probabilities are proposed to regulate processors’ modes. Through the design of appropriate sliding functions, feedback gain matrices, and observer gain matrices, our results demonstrate that both the estimation errors and states in the closed-loop system exhibit mean-square exponentially ultimate boundedness. Additionally, sufficient conditions are presented to establish the reachability of the selected sliding surface. Implementation algorithms are outlined based on these results, followed by simulation studies illustrating the effectiveness of the proposed design techniques.