Robust stabilization for uncertain discrete singular systems

Abstract

This paper considers the problem of robust stabilization for uncertain discrete singular systems subject to time-invariant norm-bounded unstructured uncertainty in the state matrix. The problem we address is the design of state feedback controllers such that the resulting closed-loop system is regular, causal as well as stable for all admissible uncertainties. In this connection, the concept of `generalized quadratic stabilizability' is defined. In terms of matrix inequalities, a necessary and sufficient condition for generalized quadratic stabilizability is derived under certain assumptions. When this condition holds, the explicit formula of a state feedback controller solving the problem is also given. The results can be viewed as extensions of existing results on robust stabilization of uncertain discrete standard state-space systems.