Guaranteed cost control design for descriptor systems with time-varying delays

Abstract

Motivated by a real problem in cold rolling of steel, we propose a design methodology of guaranteed cost controllers for descriptor type systems in presence of multiple time-varying delays. We first analyse the existence and uniqueness of solutions for the class of systems under study. This enable us to define the compatible initial conditions for this class of systems and show that for the closed-loop dynamics they depend on the controller. Consequently, we provide a methodology to avoid this dependency. Secondly, we consider the problem of designing a controller that stabilizes the system and ensures some performance guarantees. The proposed solution consists of minimizing a cost function related to the energetic aspects of the system. The main tool used for the control design is a modified Lyapunov-Krasovskii functional that takes into account the singularity of the system. Our solution can be easily implemented since the controller is obtained by solving some linear matrix inequalities (LMIs). A numerical example illustrates the implementation of our results.