Reduced-order proper H∞ controllers for descriptor systems: Existence conditions and LMI-based design algorithms

• Published in: 2007 46th IEEE Conference on Decision and Control pp. 6082 - 6087
• Main Authors: Xin Xin, Hara, S., Kaneda, M.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2007
• Subjects: Algorithm design and analysis; Application software; Computer science; Control systems; Filtering theory; Information science; Physics computing; Systems engineering and theory; USA Councils
• ISBN: 9781424414970; 1424414970
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2007.4434574

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