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

Wassim M. Haddad; VijaySekhar Chellaboina; Sergey G. Nersesov

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Impulsive and Hybrid Dynamical Systems

Stability, Dissipativity, and Control

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Language: English

Published/Copyright: 2014

About this book

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.

Author / Editor information

Wassim M. Haddad is Professor of Aerospace Engineering at the Georgia Institute of Technology. VijaySekhar Chellaboina is Associate Professor of Mechanical, Aerospace, and Biomedical Engineering at the University of Tennessee. Sergey G. Nersesov is Assistant Professor of Mechanical Engineering at Villanova University. Haddad, Chellaboina, and Nersesov previously coauthored Thermodynamics: A Dynamical Systems Approach (Princeton).

Reviews

"This book fills a void in the are of systems research and is a welcome addition to the literature on hybrid and impulsive systems. The book is well organized, well written, and rigorous in the development of their subject on hand. The authors are to be commended for their scholarly contribution on a subject that is still evolving."---Anthony N. Michel, IEEE Control Systems Magazine --- "With the growing interest in hybrid dynamical systems, the book forms a welcome text dealing with a restricted well-defined class of hybrid systems. Typical subjects that receive attention throughout are set-stability, energy based control, inverse-optimal control, etc. The book may be viewed as a welcome addition in the areas of hybrid systems, containing rigorous and detailed results."---Henk Nijmeijer, Mathematical Reviews --- "Wassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics"

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Publicly Available

Frontmatter
i

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Contents
ix

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Preface
xiii

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Chapter One. Introduction
1

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Chapter Two. Stability Theory for Nonlinear Impulsive Dynamical Systems
9

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Chapter Three. Dissipativity Theory for Nonlinear Impulsive Dynamical Systems
81

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Chapter Four. Impulsive Nonnegative and Compartmental Dynamical Systems
125

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Chapter Five. Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems
147

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Chapter Six. Stability and Feedback Interconnections of Dissipative Impulsive Dynamical Systems
191

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Chapter Seven. Energy-Based Control for Impulsive Port-Controlled Hamiltonian Systems
221

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Chapter Nine. Optimal Control for Impulsive Dynamical Systems
319

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Chapter Ten. Disturbance Rejection Control for Nonlinear Impulsive Dynamical Systems
351

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Chapter Eleven. Robust Control for Nonlinear Uncertain Impulsive Dynamical Systems
385

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Chapter Twelve. Hybrid Dynamical Systems
411

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Chapter Thirteen. Poincare Maps and Stability of Periodic Orbits for Hybrid Dynamical Systems
443

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Appendix A. System Functions for the Clock Escapement Mechanism
477

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Bibliography
485

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Index
501

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

September 8, 2014

eBook ISBN:

9781400865246

Pages and Images/Illustrations in book

https://doi.org/10.1515/9781400865246

eBook ISBN: 9781400865246

Keywords for this book

Dynamical system; Instability; Differentiable function; Nonlinear system; Negative feedback; Lyapunov function; Nonlinear programming; Dissipation; Dissipative system; Hybrid system; Moment of inertia; Special case; Limit cycle; Small-gain theorem; Linearization; Mathematical optimization; Vibration; Boundedness; Escapement; Monotonic function; Uncertainty; Limit set; Continuous function; Asymptotic analysis; Stability theory; Lyapunov stability; Arbitrarily large; Differential equation; Interconnection; Parameter; Optimal control; Asymptote; Nonnegative matrix; Stiffness; Passive dynamics; Invariance theorem; Control theory; Hamiltonian mechanics; Inequality (mathematics); Orthant; Mass balance; Equilibrium point; Axiom; Dynamical systems theory; Linear function; Lipschitz continuity; Equations of motion; Calculation; Bode plot; Iterative method; Infimum and supremum; Mixture; State space; Transpose; Analog computer; Poincaré conjecture; Semi-infinite; Amplitude; Melting; Hamiltonian system; Vector field; Ordinary differential equation; Theorem; Adaptive control; Partial differential equation; Zeroth law of thermodynamics; Proof mass; Robust control; Identity matrix; Lagrangian (field theory)

Audience(s) for this book

For an expert adult audience, including professional development and academic research

Princeton University Press

Impulsive and Hybrid Dynamical Systems

Overview

About this book

Author / Editor information

Reviews

Topics

Table of contents

Frontmatter

Contents

Preface

Chapter One. Introduction

Chapter Two. Stability Theory for Nonlinear Impulsive Dynamical Systems

Chapter Three. Dissipativity Theory for Nonlinear Impulsive Dynamical Systems

Chapter Four. Impulsive Nonnegative and Compartmental Dynamical Systems

Chapter Five. Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems

Chapter Six. Stability and Feedback Interconnections of Dissipative Impulsive Dynamical Systems

Chapter Seven. Energy-Based Control for Impulsive Port-Controlled Hamiltonian Systems

Chapter Nine. Optimal Control for Impulsive Dynamical Systems

Chapter Ten. Disturbance Rejection Control for Nonlinear Impulsive Dynamical Systems

Chapter Eleven. Robust Control for Nonlinear Uncertain Impulsive Dynamical Systems

Chapter Twelve. Hybrid Dynamical Systems

Chapter Thirteen. Poincare Maps and Stability of Periodic Orbits for Hybrid Dynamical Systems

Appendix A. System Functions for the Clock Escapement Mechanism

Bibliography

Index

Bibliographic data