Sliding mode control of two-dimensional systems in Roesser model

The study is concerned with the problem of sliding mode control of two-dimensional (2D) discrete systems. Given a 2D system in Roesser model, attention is focused on the design of sliding mode controllers, which guarantee the resultant closed-loop systems to be asymptotically stable. This problem is solved by using two different methods: model transformation method and Choi´s 1997 method. In terms of linear matrix inequality, sufficient conditions are formulated for the existence of linear switching surfaces guaranteeing asymptotic stability of the reduced-order equivalent sliding mode dynamics. Based on this, the problem of controller synthesis is investigated, with two different controller design procedures proposed, which can be easily implemented by using standard numerical software. A numerical example is provided to illustrate the effectiveness of the proposed controller design methods.