The Dissipation Inequality and Generalized Algebraic Riccati Equation for Linear Quadratic Control Problem of Descriptor System

Abstract

We consider the infinite-horizon linear quadratic control problems (LQCPs) for a descriptor system based on the theory of dissipative system. We derive a dissipation inequality (DI) for the descriptor system satisfied by the optimal costs. It is shown that the optimal costs can be characterized by the solution of the LMI and that a related generalized algebraic Riccati equation (GARE) has solutions under the regularity condition. Finally, the optimal solution to the LQCP with zero terminal condition is derived.