Robust stabilization of descriptor linear systems via proportional-plus-derivative state feedback

A sufficient condition, in terms of quadratic stability of matrices, for the class of regular descriptor linear systems which possess no infinite relative eigenvalues is presented. Utilizing this result, the problem of stabilization of descriptor linear system via proportional-plus-derivative (PD) state feedback control is converted into two related quadratically stabilization problems, which can be easily solved using linear matrix inequality (LMI) techniques. Based on the same idea, robust stabilization via PD state feedback for uncertain descriptor linear systems, with coefficient matrices belonging to some compact sets in proper matrix spaces, has also been dealt with.