Continuous-time H2 optimal control problem for descriptor systems

in this paper we consider the full information and the semistate feedback H-2 control problems for continuous- time descriptor systems. An explicit characterization of all optimal controllers has been given for these cases. We present also a parametrization of all optimal static and dynamic controllers for the LQR problem via semi-state feedback. We show that, for the general semi-state feedback H-2 optimization, the usual gain matrix defined as a linear function of a solution of a generalized Riccati equation can be not H-2-optimal. This contrasts with the classical results in LQR theory for descriptor systems and with the results of H-2 theory in regular state-space framework.