On the generalized algebraic Riccati equation for continuous-time descriptor systems

Abstract In this paper we consider the generalized algebraic Riccati equation (GARE) for a continuous-time descriptor system. Necessary and sufficient conditions for the existence of stabilizing solutions of the GARE are derived based on the Hamiltonian matrix pencil approach. A parametrization of all stabilizing solutions is also provided. The main result has a potential applicability to a wide class of control problems for a descriptor system, including H 2 / H ∞ controls.