Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities

In this work, the problem of asynchronous sliding mode control (SMC) is investigated for a class of uncertain Markovian jump systems (MJSs) with time-varying delays and stochastic perturbation. It is assumed that the system modes cannot be obtained synchronously by the controller, but instead there is a detector that provides estimated values of the system modes. This asynchronous phenomenon between the system modes and controller modes will be described in this work via a hidden Markov model with partly accessible mode detection probabilities. Based on a common sliding surface, an asynchronous SMC law depending on the detector mode is synthesized to ensure the mean square stability of the sliding mode dynamics and the reachability of the specified sliding surface simultaneously. Moreover, a design algorithm for obtaining the asynchronous SMC law is established. Finally, an application of the automotive electronic throttle system is provided to illustrate the effectiveness and advantages of the proposed asynchronous sliding mode control approach.