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.

In the paper, the problem of ℋ_∞ filtering for a class of linear uncertain systems is studied. The parameter uncertainties are assumed to reside in a polytope. The paper is focused on the design of a parameter-dependent filter which guarantees the filtering error system to be asymptotically stable and has a prescribed ℋ_∞ performance. By employing a parameter-dependent Lyapunov function approach, sufficient conditions are established for the existence of the desired filters in terms of linear matrix inequalities, which can be handled easily by using the available toolbox. Both continuous- and discrete-time cases are investigated. It is shown, via a numerical example, that the proposed filter design methods are more effective and less conservative than some existing results.