Sliding mode control of uncertain FMII 2D systems under directional event‐triggered schemes

Abstract

AbstractThis article is concerned with the event‐triggered sliding mode control problem for two‐dimensional (2D) systems depicted by the second Fornasini–Marchesini (FMII) model. By considering the structural characteristics of FMII 2D systems, three event‐triggering schemes in one or two directions are analyzed and the corresponding partial ordering on pairs of triggering instants are given. In particular, the two‐directional event‐triggering scheme reflects the essential difference between FMII model and Roesser model. Accordingly, a two‐directional event‐triggered mechanism from sensors to controller is developed and the event‐triggered sliding mode controller is designed. Since the FMII 2D model is affected by two adjacent control signals, the updation of the control signals at two points and is detailedly discussed. Both the reachability of the sliding surface and the uniform ultimate boundedness of the resultant closed‐loop system are achieved. Meanwhile, the desired controller gain matrix and sliding matrix are determined by solving stability conditions. Finally, the proposed control scheme is further demonstrated via the heat exchanger process.