A straightforward approach to state-space controllers for descriptor systems: H ∞ controller design via LMIs

Abstract This paper proposes a straightforward approach to direct design of state-space controllers for descriptor systems. The term “direct design” is used to distinguish the idea of this paper from the usual way through descriptor-type controllers, which has been extensively developed for these two decades. A necessary and sufficient condition is derived for the existence of a strictly proper state-space output feedback controller which makes the closed-loop descriptor system regular, impulse-free, stable, and its H ∞ norm less than a specified value. The condition is expressed in terms of linear matrix inequalities (LMIs) and their solutions give coefficient matrices of the state-space H ∞ controllers.