Robust Stabilization of Linear Descriptor Systems

A Quadratic Stabilization Approach to Equivalent Systems

Abstract

This paper presents conditions for a linear uncertain descriptor system to be robustly stabilizable via linear feedback control. It is assumed that the system has a fixed number of exponential modes, but no impulsive mode. Applying the quadratic stabilization approach to tractable equivalent systems, robust stabilizability conditions for a system with polytopic uncertainties are obtained in terms of linear and bilinear matrix inequalities. An algorithm based on the idea of the homotopy method is proposed to solve the bilinear matrix inequality.