A descriptor system approach to H∞ control of linear timedelay systems

Abstract—The output-feedback control problem is solved for continuous-time, linear, retarded and neutral type systems. A delay-dependent solution is obtained in terms of linear matrix in-equalities (LMIs) by using a descriptor model transformation of the system and by applying Park’s inequality for bounding cross terms. A state-feedback solution is derived for systems with poly-topic parameter uncertainties. An output-feedback controller is then found by solving two LMIs, one of which is associated with a descriptor time-delay “innovation filter. ” The cases of instanta-neous and delayed measurements are considered. Numerical exam-ples are given which illustrate the effectiveness of the new theory. Index Terms—Delay-dependent criteria, descriptor systems,-control, linear matrix inequalities (LMIs), time-delay sys-tems. I