H-Infinity Control for Nonlinear Descriptor Systems

The authors present a study of the H-infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. They derive necessary and sufficient conditions for the existence of a controller solving the standard nonlinear H-infinity control problem considering both state feedback and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of two Hamilton-Jacobi inequalities and a weak coupling condition; a parameterization of a family of output feedback controllers solving the problem is also provided. All of the aforementioned results are then specialized to the linear case. For the linear case, the necessary and sufficient conditions for the corresponding problems to be solvable are expressed in terms of two hierarchically coupled generalized algebraic Riccati equations. When these conditions hold, state-space formulae for a controller solving the problem are also given. The approach used in this monograph is based on a generalized version of the Bounded Real Lemma. Finally, the derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. To establish the key formulae, a parameterization of all internally stabilizing controllers for descriptor systems is also given (both the linear and nonlinear cases are considered in this monograph). Among other important topics to be investigated are the balanced realization, reduced-order controller design and mixed H2/H-infinity control problems. For students and researchers interested in nonlinear control theory for descriptor systems, this book provides both a comprehensive introduction and easy access to advanced topics.

From the reviews: "The monograph presents a study of the H infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. The target group of the monograph is aimed to be academic researchers in control theory, nonlinear systems and control engineering. Necessary and sufficient conditions are derived for the existence of a controller solving the standard nonlinear H infinity control problem considering both state feedback and output feedback." (Ilkka Virtanen, Zentralblatt MATH, Vol. 1113 (15), 2007)

Chee-Fai Yung has been with the Department of Electrical Engineering, National Taiwan Ocean University, where he is currently a Professor since August 1993. He was an Associate Professor with the Department of Electric Engineering, National Taiwan Institute of Technology from 1988 to 1999. He has been the editor of Journal of Nonlinear Studies since 2001. He received the Excellent Research Award in 2000 from the Taiwanese National Science Council. His main research interests are robust control, nonlinear control, H-infinity control, descriptor systems theory, PC-based real-time control and applications.   From 1976 to 1981, Fan-Ren Chang was an assistant researcher of Chung Shan Institute of Science and Technology. He worked for missile and fire control system projects. He joined the Department of Electrical Engineering, National Taiwan University in 1985 as an Associate Professor. Since 1990, he has been a Professor at the same department. His research interests include linear multivariable systems, generalized systems, numerical algorithms, and satellite navigation systems.

Introduction.- Elements of Descriptor Systems Theory.- Youla Parameterization.- The H-infinity Control.- Balanced Realization.- Some Further Topics.- Conclusions.- Appendices: Generalized Algebraic Riccati Equations; Center Manifold Theory.