Robust observer-based sliding mode H∞ control for stochastic Markovian jump systems subject to packet losses

Abstract This paper studies the robust observer-based sliding mode H ∞ control issue for discrete-time stochastic Markovian jumping systems (MJSs) subject to packet losses (PLs). Here, a state variable observer of an initial system is designed to estimate the state and a series of Bernoulli random variables is utilized to model the PLs, whose occurrence probability is allowed to be imprecise. Then, a linear switching function is constructed based on the estimated state space. The aim of our paper is to design an observer-based sliding mode H ∞ control strategy such that, the stochastic stability conditions with prescribed H ∞ performance are established for augmented MJSs under the PLs with imprecise occurrence probability, which is composed of the sliding mode dynamics and the error system. The linear sliding surface can be determined by solving some linear matrix inequalities (LMIs). In addition, by proposing an improved reaching condition, the desired robust observer-based H ∞ controller is designed in discrete-time setting to drive the system state from any initial one onto the designated sliding surface. Finally, the usefulness of observer-based H ∞ control method is demonstrated via some numerical simulations.