Robust Stabilization for a Class of Uncertain Descriptor Systems via Both Proportional and Derivative State Feedback

Firstly, the problem of robust stability is studied for a class of descriptor systems with structured uncertainties, whose nominal systems are normalizable. With linear matrix inequality (LMI), the equivalent existence condition of both proportional and derivative (P-D) state feedback is given , which results in the optimization problem. furthermore, a necessary and sufficient condition of robust quadratic stabilization will be obtained by introducing a fictitious input and a useful lemma. Finally, based on the equivalent condition, two algorithms for robust stabilizing controller are derived by solving the corresponding LMIs.