Robust Dissipative Control and Filtering for 2-D Discrete-Time Switched Systems with Time-Varying Delays

This paper studies dissipative control and filtering for a two-dimensional (2-D) nonlinear switched system with polytopic uncertainties and time-varying delays described by the Fornasini-Marchesini (FM) model. The nonlinearities are decomposed into linear forms under the Takagi-Sugeno (T-S) fuzzy rules. Assuming that uncertain parameters belong to a convex, bounded polyhedral domain, a parameter-dependent multiple Lyapunov-Krasovskii functional (MLKF) is established. Additionally, some free-weighting matrices that depend on the switching signal are introduced. This provides a new sufficient condition that exhibits reduced conservatism for the robust dissipative performance analysis of 2-D nonlinear polytopic uncertain switched systems. Furthermore, the design of parameter-independent and parameter-dependent state feedback controllers and filters for the system is investigated based on the proposed sufficient condition. Finally, three numerical examples are provided to validate our methods and demonstrate the reduced conservatism of our approach.