For a class of switched discrete-time linear systems, a state-dependent switching law with dwell time is designed to make the overall system asymptotically stable. A main feature is that the Lyapunov-like function may not be monotonically decreasing in both time-driven and state-driven periods, and this feature allows the proposed stabilising switching law being of lower switching frequency in contrast with recent results. An illustrative example is employed to show the effectiveness of the proposed switching law. Furthermore, it is shown that the proposed switching law ensures that a bounded perturbation implies bounded states, and a convergent perturbation implies convergent states. When the system state is not available, an observer-based state-dependent switching law with dwell time is also developed.

The problem of delay-dependent robust energy-to-peak filtering design for a class of discrete-time switched linear systems with a time-varying state delay and polytopic uncertainties is revisited. The objective is to design a homogeneous switched linear filter guaranteeing the exponential stability of the resulting filtering error system with a minimised robust energy-to-peak disturbance attenuation level under average dwell-time switching scheme. Based on a novel delay and parameter-dependent discontinuous switched Lyapunov–Krasovskii functional combined with Finsler's lemma, a new sufficient condition for robust exponential stability and energy-to-peak performance analysis is first derived and then the corresponding filter synthesis is developed. It is shown that the filter parameters can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the advantages and less conservatism of the proposed approach in comparison with the existing approaches.

Issues of observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay and disturbance input are addressed, where the Lipschitz condition is expressed in a componentwise rather than aggregated manner. It has been shown that both full-order and reduced-order robust H_∞ observers can be obtained by means of the same convex optimisation procedure with minimisation of the disturbance attenuation upper bound γ>0. It is also shown that for a prescribed H_∞-norm upper bound γ>0, the tolerable Lipschitz bounds can be obtained by another convex optimisation procedure. A numerical example is presented to show the effectiveness of the developed approach.

A generalised H₂ controller synthesis method for discrete-time fuzzy systems based on a piecewise Lyapunov function is presented. The basic idea of the proposed approach is to construct a controller for the discrete-time fuzzy systems in such a way that a piecewise Lyapunov function can be used to establish global stability with generalised H₂ performance for the resulting closed-loop fuzzy control systems. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities that are numerically tractable with commercially available software. An example is presented to demonstrate the advantage of the proposed approach.