Observer-based control of uncertain nonlinear Markovian jump systems with time-varying delay and actuator failures via sliding mode technique

This paper focuses on the discussion of asynchronous sliding mode control (SMC) design for uncertain Markovian jump systems (MJSs) in which nonlinearities, time-varying delays, and actuator failures are considered. At first, the study establishes an asynchronous observer and correspondingly constructs a sliding mode switching function in which the controller gain operates asynchronously with the original system. Then the observer-based SMC law is designed through Lyapunov stability theory to achieve reachability of the specified sliding surface, resulting in mean-square stability of the closed-loop system. In addition, we extend the aforementioned findings to a more practical case where the conditional probability is only partially known. Eventually, numerical examples and tunnel-diode-circuit examples are provided to demonstrate the merits of the summarized results.