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Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control

Wassim M. Haddad, VijaySekhar Chellaboina, and Sergey G. Nersenov
Publisher: 
Princeton University Press
Publication Date: 
2006
Number of Pages: 
504
Format: 
Hardcover
Series: 
Princeton Series in Applied Mathematics
Price: 
69.50
ISBN: 
0691127158
Category: 
Monograph
We do not plan to review this book.

Preface xiii

Chapter 1. Introduction 1
1.1 Impulsive and Hybrid Dynamical Systems 1
1.2 A Brief Outline of the Monograph 4

Chapter 2. Stability Theory for Nonlinear Impulsive Dynamical Systems 9
2.1 Introduction 9
2.2 Nonlinear Impulsive Dynamical Systems 11
2.3 Stability Theory of Impulsive Dynamical Systems 20
2.4 An Invariance Principle for State-Dependent Impulsive Dynamical Systems 27
2.5 Necessary and Sufficient Conditions for Quasi-Continuous Dependence 32
2.6 Invariant Set Theorems for State-Dependent Impulsive Dynamical Systems 38
2.7 Partial Stability of State-Dependent Impulsive Dynamical Systems 44
2.8 Stability of Time-Dependent Impulsive Dynamical Systems 56
2.9 Lagrange Stability, Boundedness, and Ultimate Boundedness 63
2.10 Stability Theory via Vector Lyapunov Functions 71

Chapter 3. Dissipativity Theory for Nonlinear Impulsive Dynamical Systems 81
3.1 Introduction 81
3.2 Dissipative Impulsive Dynamical Systems: Input-Output and State Properties 84
3.3 Extended Kalman-Yakubovich-Popov Conditions for Impulsive Dynamical Systems 103
3.4 Specialization to Linear Impulsive Dynamical Systems 119

Chapter 4. Impulsive Nonnegative and Compartmental Dynamical Systems 125
4.1 Introduction 125
4.2 Stability Theory for Nonlinear Impulsive Nonnegative Dynamical Systems 126
4.3 Impulsive Compartmental Dynamical Systems 131
4.4 Dissipativity Theory for Impulsive Nonnegative Dynamical Systems 135
4.5 Specialization to Linear Impulsive Dynamical Systems 143

Chapter 5. Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems 147
5.1 Introduction 147
5.2 Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems 150
5.3 Extended Kalman-Yakubovich-Popov Conditions for Large-Scale Impulsive Dynamical Systems 175
5.4 Specialization to Large-Scale Linear Impulsive Dynamical Systems 186

Chapter 6. Stability and Feedback Interconnections of Dissipative Impulsive Dynamical Systems 191
6.1 Introduction 191
6.2 Stability of Feedback Interconnections of Dissipative Impulsive Dynamical Systems 191
6.3 Hybrid Controllers for Combustion Systems 199
6.4 Feedback Interconnections of Nonlinear Impulsive Nonnegative Dynamical Systems 208
6.5 Stability of Feedback Interconnections of Large-Scale Impulsive Dynamical Systems 214

Chapter 7. Energy-Based Control for Impulsive Port-Controlled Hamiltonian Systems 221
7.1 Introduction 221
7.2 Impulsive Port-Controlled Hamiltonian Systems 222
7.3 Energy-Based Hybrid Feedback Control 227
7.4 Energy-Based Hybrid Dynamic Compensation via the Energy-Casimir Method 233
7.5 Energy-Based Hybrid Control Design 242

Chapter 8. Energy and Entropy-Based Hybrid Stabilization for Nonlinear Dynamical Systems 249
8.1 Introduction 249
8.2 Hybrid Control and Impulsive Dynamical Systems 251
8.3 Hybrid Control Design for Dissipative Dynamical Systems 258
8.4 Lagrangian and Hamiltonian Dynamical Systems 265
8.5 Hybrid Control Design for Euler-Lagrange Systems 267
8.6 Thermodynamic Stabilization 271
8.7 Energy-Dissipating Hybrid Control Design 277
8.8 Energy-Dissipating Hybrid Control for Impulsive Dynamical Systems 300
8.9 Hybrid Control Design for Nonsmooth Euler-Lagrange Systems 308
8.10 Hybrid Control Design for Impact Mechanics 313

Chapter 9. Optimal Control for Impulsive Dynamical Systems 319
9.1 Introduction 319
9.2 Impulsive Optimal Control 319
9.3 Inverse Optimal Control for Nonlinear Affine Impulsive Systems 330
9.4 Nonlinear Hybrid Control with Polynomial and Multilinear Performance Functionals 333
9.5 Gain, Sector, and Disk Margins for Optimal Hybrid Regulators 337
9.6 Inverse Optimal Control for Impulsive Port-Controlled Hamiltonian Systems 345

Chapter 10. Disturbance Rejection Control for Nonlinear Impulsive Dynamical Systems 351
10.1 Introduction 351
10.2 Nonlinear Impulsive Dynamical Systems with Bounded Disturbances 352
10.3 Specialization to Dissipative Impulsive Dynamical Systems with Quadratic Supply Rates 358
10.4 Optimal Controllers for Nonlinear Impulsive Dynamical Systems with Bounded Disturbances 366
10.5 Optimal and Inverse Optimal Nonlinear-Nonquadratic Control for Affine Systems with L2 Disturbances 375

Chapter 11. Robust Control for Nonlinear Uncertain Impulsive Dynamical Systems 385
11.1 Introduction 385
11.2 Robust Stability Analysis of Nonlinear Uncertain Impulsive Dynamical Systems 386
11.3 Optimal Robust Control for Nonlinear Uncertain Impulsive Dynamical Systems 395
11.4 Inverse Optimal Robust Control for Nonlinear Affine Uncertain Impulsive Dynamical Systems 402
11.5 Robust Nonlinear Hybrid Control with Polynomial Performance Functionals 406

Chapter 12. Hybrid Dynamical Systems 411
12.1 Introduction 411
12.2 Left-Continuous Dynamical Systems 412
12.3 Specialization to Hybrid and Impulsive Dynamical Systems 418
12.4 Stability Analysis of Left-Continuous Dynamical Systems 422
12.5 Dissipative Left-Continuous Dynamical Systems: Input-Output and State Properties 427
12.6 Interconnections of Dissipative Left-Continuous Dynamical Systems 435

Chapter 13. Poincar´e Maps and Stability of Periodic Orbits for Hybrid Dynamical Systems 443
13.1 Introduction 443
13.2 Left-Continuous Dynamical Systems with Periodic Solutions 444
13.3 Specialization to Impulsive Dynamical Systems 451
13.4 Limit Cycle Analysis of a Verge and Foliot Clock Escapement 458
13.5 Modeling 459
13.6 Impulsive Differential Equation Model 462
13.7 Characterization of Periodic Orbits 464
13.8 Limit Cycle Analysis of the Clock Escapement Mechanism 468
13.9 Numerical Simulation of an Escapement Mechanism 472

Appendix A. System Functions for the Clock Escapement Mechanism 477

Bibliography 485
Index 501

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