Lecture Notes in Control and Information Sciences

By: He-Sheng Wang, Chee-Fai Yung, Fan-Ren Chang

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Paperback | 18 January 2006

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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.

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"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)

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You Can Find This Book In

Non-Fiction Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory Engineering & Technology Energy Technology & Engineering Electrical Engineering Mathematics Applied Mathematics Electronics & Communications Engineering Electronics Engineering

Automatic Control Engineering Robotics Computing & I.T.Computer Science Systems Analysis & Design

List of Figures	p. XI
List of Notation	p. XIII
Introduction	p. 1
Why Differential-Algebraic Equations?	p. 1
Control Problems Based on DAEs	p. 7
Highlights of the Monograph	p. 10
Elements of Descriptor Systems Theory	p. 13
Differential Algebraic Equations	p. 13
Stability, Controllability and Observability	p. 17
Lyapunov Stability Theorems	p. 21
Dissipative Descriptor Systems	p. 28
Youla Parameterization	p. 37
Nonlinear Case	p. 37
Linear Case	p. 42
An Application of the Youla Parameterization	p. 47
Positive Real Control Problem	p. 47
Characterization of All ESPR Output Feedback Controllers	p. 56
The H∞ Control	p. 61
State Feedback H∞ Control	p. 62
Output Feedback	p. 63
Parameterization of All Controllers	p. 67
Linear Case	p. 73
Converse Result-A Necessary Condition for the Nonlinear Problem	p. 82
Balanced Realization	p. 89
Balanced Realization	p. 89
Model Reduction via Balanced Truncation	p. 99
Network Synthesis	p. 103
Some Further Topics	p. 111
An Algebraic Approach to Reduced-Order Controller Design	p. 111
GARE Approach to the Linear Problem	p. 117
Mixed H₂ and H∞ Control Problems	p. 123
Problem Formulation	p. 124
Solution via State Feedback	p. 126
Solution via Static Output Feedback	p. 129
Generalization to Nonlinear Systems	p. 133
Conclusions	p. 137
Concluding Remarks	p. 137
An Open Problem for DAEs	p. 139
Generalized Algebraic Riccati Equations	p. 141
Center Manifold Theory	p. 149
References	p. 153
Index	p. 163
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Lecture Notes in Control and Information Sciences

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