Generalized Quadratic Stabilization for Perturbated Discrete-time Singular Systems with Delayed State

This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular system with time-delay and nonlinear perturbation (DSSDP) which satisfies Lipschitz condition. By means of Sprocedure approach, necessary and sufficient condition is presented via matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of 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 general DSSDP.