Reliable controller design for admissibility of uncertain discrete-time singular system with time-varying delay

In this paper, we consider the delay-dependent reliable control for uncertain discrete-time singular systems with time-varying delay. By constructing a Lyapunov-Krasovskii functional together with free weighting matrix technique, delay-dependent conditions are presented for the existence of a reliable controller which ensures the singular system to be regular, causal and stable for all admissible parameter uncertainties. First, the controller for singular systems is designed for known actuator fault matrix. Further, the result is extended to the unknown actuator fault matrix. The actuator failures are described by a variable, which is varies in a given interval. All the sufficient conditions are established in the form of linear matrix inequalities (LMIs), which can be easily solved by using the standard MATLAB LMI toolbox. Finally, numerical examples are provided to illustrate the applicability and less conservatism of the proposed results.