Continuous-time H2 optimal control problem for descriptor systems

We consider the full information and the semi-state feedback H₂ 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 H₂ optimization, the usual gain matrix defined as a linear function of a solution of a generalized Riccati equation can be not H₂-optimal. This contrasts with the classical results in LQR theory for descriptor systems and with the results of H₂ theory in regular state-space framework