Protocol-based asynchronous sliding mode control for Markovian jump systems under random sampling

This paper considers the sliding mode control problem for Markovian jump systems with random switched sampling periods, in which the transmission of sampled states is regulated via a stochastic scheduling protocol for reducing communication network congestion. By utilizing a mode detector, an asynchronous sliding mode controller is designed via transmitted sampled states. Besides, the feature of random sampling is described by introducing delays, whose corresponding probabilities falling within each sampling interval are explicitly given. Then, a multi-delays closed-loop system with stochastic parameters is established, and its stability is analyzed in the light of the looped-functional analysis method. Furthermore, an optimized solving algorithm on controller gain is proposed with the objective of achieving a small sliding region. Finally, simulation results are provided to illustrate the effectiveness of the designed sliding mode sampled scheme.