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Liapunov Functions and Stability in Control Theory Second Edition 2005 [Kõva köide]

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  • Formaat: Hardback, 237 pages, kõrgus x laius: 235x155 mm, kaal: 1170 g, XIII, 237 p., 1 Hardback
  • Sari: Communications and Control Engineering
  • Ilmumisaeg: 13-Apr-2005
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540213325
  • ISBN-13: 9783540213321
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Liapunov Functions and Stability in Control Theory Second Edition 2005Suurem pilt
  • Formaat: Hardback, 237 pages, kõrgus x laius: 235x155 mm, kaal: 1170 g, XIII, 237 p., 1 Hardback
  • Sari: Communications and Control Engineering
  • Ilmumisaeg: 13-Apr-2005
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540213325
  • ISBN-13: 9783540213321
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783540213321.html
Märksõnad:
This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control. Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs. In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g., about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems. Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as mathematicians.

Arvustused

Review in amazon:



Super Book December 16, 2002 P, Princeton: Bacciotti and Rosier have managed to present a nonformal, yet rigorous and well-organized introduction to nonlinear stabilization and controllability. They have definetly captured the most important research trends in the area and have managed to cover a wide range of topics with appropriate deepness. My only suggestion would be to add a list of symbols to the book and to discuss Chow's Theorem and the accessibility rank condition. Thanks for a great book!



From the reviews of the second edition:









"This book has been written by famous scientists in the areas of stability and control theories. It presents a modern and self-contained treatment of the Lyapunov method for stability analysis in the framework of mathematical nonlinear control theory. In the 2nd edition of this successful book several new sections have been added and old sections have been improved. A lot of new examples, explanations and figures are added making this book accessible and well readable for engineers as well as mathematicians." (Alexander O. Ignatyev, Zentralblatt MATH, Vol. 1078, 2006)

Muu info

2nd edition
Preface V
1 Differential equations 1(18)
1.1 Recall about existence results
2(2)
1.2 Differential inclusions
4(9)
1.2.1 The upper semi-continuous case
4(4)
1.2.2 The Lipschitz continuous case
8(5)
1.3 Appendix
13(6)
2 Time invariant systems 19(70)
2.1 The linear case
19(8)
2.1.1 Stability
19(3)
2.1.2 Internal stabilization
22(1)
2.1.3 External stabilization
23(1)
2.1.4 Quadratic forms
24(3)
2.2 Nonlinear systems: stability
27(35)
2.2.1 Internal notions
27(3)
2.2.2 Converse theorems
30(7)
2.2.3 Generalized Liapunov functions
37(2)
2.2.4 Absolute stability
39(5)
2.2.5 Stability and robustness
44(3)
2.2.6 The Invariance Principle
47(2)
2.2.7 The domain of attraction
49(6)
2.2.8 Comparison functions
55(3)
2.2.9 External notions
58(4)
2.3 Nonlinear systems: stabilization
62(17)
2.3.1 Necessary condition for internal stabilization
63(5)
2.3.2 Asymptotic controllability and local controllability
68(2)
2.3.3 Affine systems: internal stabilization
70(7)
2.3.4 Affine systems: external stabilization
77(2)
2.4 Output systems
79(1)
2.5 Cascade systems
80(3)
2.6 Appendix
83(6)
3 Time varying systems 89(30)
3.1 Two examples
89(5)
3.2 Reformulation of the basic definitions
94(10)
3.2.1 Stability and attraction
94(7)
3.2.2 Time dependent Liapunov functions
101(3)
3.3 Sufficient conditions
104(1)
3.4 Converse theorems
105(3)
3.4.1 Asymptotic stability
105(1)
3.4.2 Uniform stability
105(3)
3.5 Robust stability
108(4)
3.6 Lagrange stability
112(1)
3.7 Discontinuous right hand side
113(1)
3.8 Time varying feedback
113(6)
4 Differential inclusions 119(48)
4.1 Global asymptotic stability
119(29)
4.1.1 Sufficient conditions
119(2)
4.1.2 Time invariant systems
121(1)
4.1.3 Time varying systems
122(3)
4.1.4 Proof of the converse of second Liapunov theorem
125(23)
4.2 Robust stability
148(13)
4.2.1 Sufficient conditions
148(4)
4.2.2 Converse of first Liapunov theorem
152(1)
4.2.3 Proof of the converse of first Liapunov theorem
153(7)
4.2.4 Application to external stabilization
160(1)
4.3 Nonsmooth Liapunov functions
161(6)
5 Additional properties of strict Liapunov functions 167(36)
5.1 Estimates for the convergence of trajectories
170(6)
5.1.1 Exponential stability
170(1)
5.1.2 Rational stability
171(4)
5.1.3 Finite-time stability
175(1)
5.2 Analyticity
176(4)
5.2.1 Analytic unsolvability of the stability problem
176(1)
5.2.2 Analytic Liapunov functions
177(3)
5.2.3 Holomorphic systems
180(1)
5.3 Weighted homogeneity
180(12)
5.3.1 A few definitions
181(2)
5.3.2 Homogeneous Liapunov functions
183(3)
5.3.3 Application to the stabilization problem
186(6)
5.4 Symmetries and Liapunov functions
192(11)
5.4.1 Discrete symmetry
193(1)
5.4.2 Infinitesimal symmetry
193(3)
5.4.3 Symmetric Liapunov functions
196(7)
6 Monotonicity and generalized derivatives 203(16)
6.1 Tools from nonsmooth analysis
203(4)
6.2 Functions of one variable
207(2)
6.3 Ordinary differential equations
209(3)
6.4 Differential inclusions
212(3)
6.5 Monotonicity and the proximal gradient
215(4)
Bibliography 219(14)
Index 233(4)
List of Abbreviations 237