Description
This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems.
Impulsive and Hybrid Dynamical Systems goes beyond similar treatments by developing invariant set stability theorems, partial stability, Lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. A major contribution to mathematical system theory and control system theory, this book is written from a system-theoretic point of view with the highest standards of exposition and rigor. It is intended for graduate students, researchers, and practitioners of engineering and applied mathematics as well as computer scientists, physicists, and other scientists who seek a fundamental understanding of the rich dynamical behavior of impulsive and hybrid dynamical systems.
Chapter
2.9 Lagrange Stability, Boundedness, and Ultimate Boundedness
2.10 Stability Theory via Vector Lyapunov Functions
Chapter 3. Dissipativity Theory for Nonlinear Impulsive Dynamical Systems
3.2 Dissipative Impulsive Dynamical Systems: Input-Output and State Properties
3.3 Extended Kalman-Yakubovich-Popov Conditions for Impulsive Dynamical Systems
3.4 Specialization to Linear Impulsive Dynamical Systems
Chapter 4. Impulsive Nonnegative and Compartmental Dynamical Systems
4.2 Stability Theory for Nonlinear Impulsive Nonnegative Dynamical Systems
4.3 Impulsive Compartmental Dynamical Systems
4.4 Dissipativity Theory for Impulsive Nonnegative Dynamical Systems
4.5 Specialization to Linear Impulsive Dynamical Systems
Chapter 5. Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems
5.2 Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems
5.3 Extended Kalman-Yakubovich-Popov Conditions for Large-Scale Impulsive Dynamical Systems
5.4 Specialization to Large-Scale Linear Impulsive Dynamical Systems
Chapter 6. Stability and Feedback Interconnections of Dissipative Impulsive Dynamical Systems
6.2 Stability of Feedback Interconnections of Dissipative Impulsive Dynamical Systems
6.3 Hybrid Controllers for Combustion Systems
6.4 Feedback Interconnections of Nonlinear Impulsive Nonnegative Dynamical Systems
6.5 Stability of Feedback Interconnections of Large-Scale Impulsive Dynamical Systems
Chapter 7. Energy-Based Control for Impulsive Port-Controlled Hamiltonian Systems
7.2 Impulsive Port-Controlled Hamiltonian Systems
7.3 Energy-Based Hybrid Feedback Control
7.4 Energy-Based Hybrid Dynamic Compensation via the Energy-Casimir Method
7.5 Energy-Based Hybrid Control Design
Chapter 8. Energy and Entropy-Based Hybrid Stabilization for Nonlinear Dynamical Systems
8.2 Hybrid Control and Impulsive Dynamical Systems
8.3 Hybrid Control Design for Dissipative Dynamical Systems
8.4 Lagrangian and Hamiltonian Dynamical Systems
8.5 Hybrid Control Design for Euler-Lagrange Systems
8.6 Thermodynamic Stabilization
8.7 Energy-Dissipating Hybrid Control Design
8.8 Energy-Dissipating Hybrid Control for Impulsive Dynamical Systems
8.9 Hybrid Control Design for Nonsmooth Euler-Lagrange Systems
8.10 Hybrid Control Design for Impact Mechanics
Chapter 9. Optimal Control for Impulsive Dynamical Systems
9.2 Impulsive Optimal Control
9.3 Inverse Optimal Control for Nonlinear Affine Impulsive Systems
9.4 Nonlinear Hybrid Control with Polynomial and Multilinear Performance Functionals
9.5 Gain, Sector, and Disk Margins for Optimal Hybrid Regulators
9.6 Inverse Optimal Control for Impulsive Port-Controlled Hamiltonian Systems
Chapter 10. Disturbance Rejection Control for Nonlinear Impulsive Dynamical Systems
10.2 Nonlinear Impulsive Dynamical Systems with Bounded Disturbances
10.3 Specialization to Dissipative Impulsive Dynamical Systems with Quadratic Supply Rates
10.4 Optimal Controllers for Nonlinear Impulsive Dynamical Systems with Bounded Disturbances
10.5 Optimal and Inverse Optimal Nonlinear-Nonquadratic Control for Affine Systems with L2 Disturbances
Chapter 11. Robust Control for Nonlinear Uncertain Impulsive Dynamical Systems
11.2 Robust Stability Analysis of Nonlinear Uncertain Impulsive Dynamical Systems
11.3 Optimal Robust Control for Nonlinear Uncertain Impulsive Dynamical Systems
11.4 Inverse Optimal Robust Control for Nonlinear Affine Uncertain Impulsive Dynamical Systems
11.5 Robust Nonlinear Hybrid Control with Polynomial Performance Functionals
Chapter 12. Hybrid Dynamical Systems
12.2 Left-Continuous Dynamical Systems
12.3 Specialization to Hybrid and Impulsive Dynamical Systems
12.4 Stability Analysis of Left-Continuous Dynamical Systems
12.5 Dissipative Left-Continuous Dynamical Systems: Input-Output and State Properties
12.6 Interconnections of Dissipative Left-Continuous Dynamical Systems
Chapter 13. Poincaré Maps and Stability of Periodic Orbits for Hybrid Dynamical Systems
13.2 Left-Continuous Dynamical Systems with Periodic Solutions
13.3 Specialization to Impulsive Dynamical Systems
13.4 Limit Cycle Analysis of a Verge and Foliot Clock Escapement
13.6 Impulsive Differential Equation Model
13.7 Characterization of Periodic Orbits
13.8 Limit Cycle Analysis of the Clock Escapement Mechanism
13.9 Numerical Simulation of an Escapement Mechanism
Appendix A. System Functions for the Clock Escapement Mechanism
Impulsive and Hybrid Dynamical Systems
：Stability, Dissipativity, and Control
( Princeton Series in Applied Mathematics )
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