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E-grāmata: Hybrid Dynamical Systems: Modeling, Stability, and Robustness

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  • Formāts: 232 pages
  • Izdošanas datums: 18-Mar-2012
  • Izdevniecība: Princeton University Press
  • Valoda: eng
  • ISBN-13: 9781400842636
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Hybrid Dynamical Systems: Modeling, Stability, and RobustnessPalielināt
  • Formāts: 232 pages
  • Izdošanas datums: 18-Mar-2012
  • Izdevniecība: Princeton University Press
  • Valoda: eng
  • ISBN-13: 9781400842636
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Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components.


With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms.


This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.



Recenzijas

"The book is carefully written and contains many examples. It will be a good resource for both researchers already familiar with hybrid systems and those starting from scratch."--Daniel Liberzon, Mathematical Reviews Clippings "The book presents a clean and self-contained exposition of hybrid systems, starting from the elementary definitions, continuing with the basic tools and finishing with more recent contributions in the literature."--Marco Castrillon Lopez, European Mathematical Society

Preface ix
1 Introduction
1(24)
1.1 The modeling framework
1(1)
1.2 Examples in science and engineering
2(5)
1.3 Control system examples
7(8)
1.4 Connections to other modeling frameworks
15(7)
1.5 Notes
22(3)
2 The solution concept
25(18)
2.1 Data of a hybrid system
25(1)
2.2 Hybrid time domains and hybrid arcs
26(3)
2.3 Solutions and their basic properties
29(6)
2.4 Generators for classes of switching signals
35(6)
2.5 Notes
41(2)
3 Uniform asymptotic stability, an initial treatment
43(30)
3.1 Uniform global pre-asymptotic stability
43(7)
3.2 Lyapunov functions
50(10)
3.3 Relaxed Lyapunov conditions
60(4)
3.4 Stability from containment
64(4)
3.5 Equivalent characterizations
68(3)
3.6 Notes
71(2)
4 Perturbations and generalized solutions
73(24)
4.1 Differential and difference equations
73(3)
4.2 Systems with state perturbations
76(3)
4.3 Generalized solutions
79(5)
4.4 Measurement noise in feedback control
84(4)
4.5 Krasovskii solutions are Hermes solutions
88(6)
4.6 Notes
94(3)
5 Preliminaries from set-valued analysis
97(20)
5.1 Set convergence
97(4)
5.2 Set-valued mappings
101(6)
5.3 Graphical convergence of hybrid arcs
107(4)
5.4 Differential inclusions
111(4)
5.5 Notes
115(2)
6 Well-posed hybrid systems and their properties
117(22)
6.1 Nominally well-posed hybrid systems
117(3)
6.2 Basic assumptions on the data
120(5)
6.3 Consequences of nominal well-posedness
125(7)
6.4 Well-posed hybrid systems
132(2)
6.5 Consequences of well-posedness
134(3)
6.6 Notes
137(2)
7 Asymptotic stability, an in-depth treatment
139(30)
7.1 Pre-asymptotic stability for nominally well-posed systems
141(7)
7.2 Robustness concepts
148(3)
7.3 Well-posed systems
151(2)
7.4 Robustness corollaries
153(3)
7.5 Smooth Lyapunov functions
156(5)
7.6 Proof of robustness implies smooth Lyapunov functions
161(6)
7.7 Notes
167(2)
8 Invariance principles
169(16)
8.1 Invariance and ω-limits
169(1)
8.2 Invariance principles involving Lyapunov-like functions
170(6)
8.3 Stability analysis using invariance principles
176(2)
8.4 Meagre-limsup invariance principles
178(3)
8.5 Invariance principles for switching systems
181(3)
8.6 Notes
184(1)
9 Conical approximation and asymptotic stability
185(14)
9.1 Homogeneous hybrid systems
185(4)
9.2 Homogeneity and perturbations
189(3)
9.3 Conical approximation and stability
192(4)
9.4 Notes
196(3)
Appendix: List of Symbols 199(2)
Bibliography 201(10)
Index 211
Rafal Goebel is an assistant professor in the Department of Mathematics and Statistics at Loyola University, Chicago. Ricardo G. Sanfelice is an assistant professor in the Department of Aerospace and Mechanical Engineering at the University of Arizona. Andrew R. Teel is a professor in the Electrical and Computer Engineering Department at the University of California, Santa Barbara.
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