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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 and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of Hamilton Jacobi inequalities and a weak coupling condition; a parameterization of output feedback controllers solving the problem is also provided. All of these results are then specialized to the linear case. The derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. Among other important topics covered are balanced realization, reduced-order controller design and mixed H2/H-infinity control. "H-infinity Control for Nonlinear Descriptor Systems" provides a comprehensive introduction and easy access to advanced topics.
List of contents
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.
About the author
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.
Summary
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 and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of Hamilton–Jacobi inequalities and a weak coupling condition; a parameterization of output feedback controllers solving the problem is also provided. All of these results are then specialized to the linear case. The derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. Among other important topics covered are balanced realization, reduced-order controller design and mixed H2/H-infinity control. "H-infinity Control for Nonlinear Descriptor Systems" provides a comprehensive introduction and easy access to advanced topics.
