Sliding Mode Control for Markovian Jump Systems With Stochastic-Sampling-Based Event-Triggered Strategy

This work focuses on the event-triggered sliding mode control problem for Markovian jump systems under the stochastic sampling that randomly switches between two sampling periods. A stochastic variable is introduced to characterize the delay between the present instant and the previous sampling instant, through which a switchinglike event-triggered strategy is proposed via the present sampled state and the previous transmitted state. Meanwhile, a mode-dependent sliding surface is constructed and a switchinglike sliding mode controller is well designed via the triggered sampled states. By means of an improved mode-dependent looped functional, sufficient conditions are obtained for the stochastic stability of the closed-loop system and the reachability of the specified sliding surface. Furthermore, an optimization problem is established and solved via the particle swarm optimization algorithm with the objective of reducing the sliding region. Finally, numerical simulation and practical example are provided to illustrate the proposed event-triggered control scheme under stochastic sampling.

I. Introduction

Most dynamical systems are subject to stochastic disturbances, including changes in external environmental conditions and internal structural variations during operation. These phenomena can be normally modeled as Markovian jump systems (MJSs), whose transition probability/rate information between different modes plays a crucial role in characterizing sudden changes. As a result, the control analysis and application of MJSs have attracted extensive attentions, such as stability analysis [1], robust control [2], optimal control [3], etc. In particular, sliding mode control (SMC) technique has emerged many interesting results for MJSs due to its strong robustness to parameter uncertainties and external disturbances, as well as its advantages of fast convergence speed [4], [5].