Direct Derivation of State-Space Controllers for H∞ Control of Descriptor Systems

This paper proposes a direct design method of state-space controllers for H∞ control of linear time-invariant descriptor systems. We derive a necessary and sufficient condition for the existence of a state-space 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 and their solutions give coefficient matrices of the state-space H∞ controllers.