Robust stabilization for uncertain discrete singular systems

This paper considers the problem of robust stabilization for uncertain disc rete singular systems subject to lime-invariant norm-bounded unstructured u ncertainty in the state matrix. The problem we address is the design of sta te feedback controllers such that the resulting closed-loop system is regul ar, causal as well as stable for all admissible uncertainties. In this conn ection. the concept of "generalized quadratic stabilizability" is defined. In terms of matrix inequalities, a necessary and sufficient condition for g eneralized quadratic stabilizability is derived under certain assumptions. When this condition holds, the explicit formula of a state feedback control ler solving the problem is also given. The results can be viewed as extensi ons of existing results on robust stabilization of uncertain discrete stand ard state-space systems. (C) 2001 Elsevier Science Ltd. All rights reserved .