H∞ control for descriptor systems: A matrix inequalities approach

Abstract

This paper considers the H ∞ control problem for descriptor systems that possibly have impulsive modes and/or jω-axis zeros. First, we propose matrix inequalities that give a generalized stability condition and an H ∞ norm condition for descriptor systems. Using these matrix inequalities, we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed H ∞ norm condition as well as stabilizing the closed-loop system and eliminating all impulsive modes. These inequalities are equivalent to certain linear matrix inequalities, to which we can get solutions whenever they exist using efficient polynomial-time algorithms.