H-infinity Control for Nonlinear Descriptor Systems

✍ Scribed by He-Sheng Wang, Chee-Fai Yung, Fan-Ren Chang

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 172
• Series: Lecture Notes in Control and Information Sciences
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

front-matter......Page 1
1.1 Why Di.erential-Algebraic Equations?......Page 12
1.2 Control Problems Based on DAEs......Page 18
1.3 Highlights of the Monograph......Page 21
2.1 Di.erential Algebraic Equations......Page 23
2.2 Stability, Controllability and Observability......Page 27
2.3 Lyapunov Stability Theorems......Page 31
2.4 Dissipative Descriptor Systems......Page 38
Notes and References......Page 45
3.1 Parameterization of All Stabilizing Controllers - Nonlinear Case......Page 47
3.2 Parameterization of All Stabilizing Controllers - Linear Case......Page 52
3.3.1 Positive Real Control Problem......Page 57
3.3.2 Characterization of All ESPR Output Feedback Controllers......Page 66
Notes and References......Page 69
4 The H¥ Control Problems......Page 71
4.1 State Feedback H ∞ Control......Page 72
4.2 Output Feedback H ∞ Control......Page 73
4.3 Parameterization of Output Feedback Controllers......Page 77
4.4 Linear Case......Page 83
4.5 Converse Result- A Necessary Condition for the Nonlinear Problem......Page 92
Notes and References......Page 97
5.1 Balanced Realization......Page 98
5.2 Model Reduction via Balanced Truncation......Page 108
5.3 Network Synthesis......Page 112
Notes and Reference......Page 117
6.1 An Algebraic Approach to Reduced-Order Controller Design......Page 119
6.1.1 GARE Approach to the Linear Problem......Page 125
6.2 Mixed H 2 and H ∞ Control Problems......Page 131
6.2.1 Problem Formulatio......Page 132
6.2.2 Solution via State Feedback......Page 134
6.2.3 Solution via Static Output Feedback......Page 137
6.2.4 Generalization to Nonlinear Systems......Page 141
Notes and References......Page 143
7.1 Concluding Remarks......Page 145
7.2 An Open Problem for DAEs[12]......Page 147
A Generalized Algebraic Riccati Equations......Page 149
B Center Manifold Theory......Page 157
back-matter......Page 160