Quadratic Stability and Quadratic Stabilization of Linear Descriptor Systems

Abstract

This paper is concerned with the quadratic stability and the quadratic stabilizability via semi-state feedback of a linear descriptor system with time-varying and norm-bounded uncertainties which lie in every coefficient matrix of the system. First, it is shown that the uncertain descriptor system under consideration can be equivalently transformed to the system without uncertainties in the coefficient matrix for the derivative of the descriptor variables, and the conformability of the transformed descriptor system is introduced, which corresponds to the property for a time-invariant descriptor system to have a unique solution and no impulsive modes. Secondly, the quadratic stability is defined and then a necessary and sufficient condition for the quadratic stability is provided based on the generalized Lyapunov theory. Finally, a necessary and sufficient condition for the quadratic stabilizability and a stabilizing controller are given. æ