The linear-quadratic optimal regulator for continuous-time descriptor systems: a dynamic programming approach

In this paper we consider the linear-quadratic optimal regulator problem for continuous-time descriptor system by the dynamic programming approach. A generalized Riccati equation is derived by making use of the Hamilton-Jacobi equation for the descriptor system. Sufficient conditions for the existence of a solution of the generalized Riccati differential (algebraic) equation are studied. It is shown that the existence of the solution of the generalized Riccati differential (algebraic) equation depends on the solutions of a standard Riccati algebraic equation and a standard Riccati differential (algebraic) equation. As in the regular state-space system, the solution of the generalized Riccati equation is used in the construction of the optimal feedback gains.