MATHEMATICAL ENGINEERING TECHNICAL REPORTS Reduced-Order Proper H∞ Controllers for Descriptor Systems: Existence Conditions and LMI-Based Design Algorithms

In this paper, we present a new approach to investigate the existence and design of reduced-order proper H∞ controllers that provide the same level of performance as that of full-order controllers. By examining some special features of the LMI-based solvability conditions for the H∞ control problem for descriptor systems, we obtain a refined bound on the order of H∞ controllers, which is independent of (invariant under the allowed transformations on) a descriptor realization of the generalized plant. Moreover, we provide two LMI-based algorithms to design reduced-order controllers; and we demonstrate the validity of the theoretical results obtained in this paper via two numerical examples. This paper not only extends in a satisfying way the results on reduced-order H∞ controllers for state-space systems to descriptor systems, but also provides insight into the mechanism by which the order of H∞ controllers for descriptor systems can be reduced through a consideration of the unstable finite zeros or infinite zeros.