Improved approach to delay-dependent stability and stabilisation of two-dimensional discrete-time systems with interval time-varying delays

Two recent Lyapunov-based methods: free weighting matrix approach and Jensen inequality approach, have reduced the conservatism and the complexity of the stability result for one-dimensional (1D) time-delay systems, respectively. In this study, the authors further concern the analysis of delay-dependent stability and stabilisation for two-dimensional (2D) discrete systems with interval time-varying delays. By applying a new Lyapunov functional combining with the approaches of 2D Jensen inequalities and free weighting matrices, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Compared with the existing result, less decision variables are involved in the stability condition, so the burden of numerical computation is reduced greatly. It is also rigorously proved that the author´s result is less conservative than some recent ones. On the basis of the stability criterion, state feedback is considered to realise the stability control and the state feedback gain can be solved by LMIs. Numerical examples show the effectiveness and advantage of their results.