Robust ℋ2 sliding mode control for non-linear discrete-time stochastic systems

Abstract

This study is concerned with the sliding mode control (SMC) problem for uncertain non-linear discrete-time stochastic systems with H 2 performance constraints. The non-linearities considered are of both the matched and unmatched forms, which can encompass several classes of well-studied non-linearities. A new discrete-time switching function is proposed and then a sufficient condition is derived which ensures both the exponentially mean-square stability and the H 2 performance in the sliding surface. Such a condition is expressed as the feasibility of a set of linear matrix inequalities (LMIs) with an equality constraint. An improved discrete-time reaching condition is established to obtain the required SMC controller capable of driving the state trajectories onto the specified switching surface, along which then resulting in a non-increasing zigzag-type sliding motion. A simulation example is given to show the effectiveness of the proposed method.