Switched discrete-time systems with time-varying delays: A generalized H2H2 approach

In this paper, we investigate the delay-dependent performance analysis and control synthesis of a class of linear discrete-time hybrid systems with time-varying delays. We employ hybrid Lyapunov–Krasovskii functionals to establish the desired results under arbitrary switching. A generalized H2H2 approach is adopted and new parameterized linear matrix inequalities (LMIs) characterization are developed to guarantee the delay-dependent asymptotic stability. Design of generalized H2H2 state feedback and dynamic output-feedback controllers are subsequently constructed. A numerical example is solved in detail to illustrate the theoretical developments.