Generalized Quadratic Stabilization for Discrete-time Singular Systems with Time-delay and Nonlinear Perturbation

This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete-time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non-singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples.