Dissipative Systems and Stability

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Table of Contents

Preface

Chapter 1. Introduction
  1. Background
  2. The notion of a dynamical system
  3. The property of passivity
  4. Taking stored energy into account
  5. Passivity and stability
  6. Finite gain systems
  7. The extension to dissipative systems
Chapter 2. Defining dissipativeness
  1. Overview
  2. The mathematical setting
  3. Signal spaces
  4. The definition of dissipativeness
  5. Ultimate virtual dissipativeness and weak dissipativeness
Chapter 3. Storage Functions
  1. Dissipativeness as a state-space property
  2. The state-space model
  3. Storage functions
  4. The relationship between external and internal dissipativeness
  5. Bounds on storage functions
  6. Positive storage functions
  7. Lossless systems
  8. More general energy functions
Chapter 4. Passive Systems
  1. Overview
  2. Passivity and stability
  3. Internal and external passivity
  4. Passivity in the frequency domain
  5. Strong passivity
  6. The single-loop stability result
Chapter 5. Algebraic conditions for dissipativeness
  1. Overview
  2. A class of nonlinear continuous-time systems
  3. The main result for continuous-time systems
  4. The question of differentiability
  5. More general nonlinear systems
  6. Linear continuous-time systems
  7. Linear discrete-time systems
Chapter 6. Stability
  1. Overview
  2. The basic stability results
  3. Interconnected systems
  4. Neutral interconnections
  5. Single-loop feedback systems
  6. Passive subsystems
  7. A small gain theorem
  8. Conic subsystems
  9. Examples
Chapter 7. Instability
  1. Criteria for instability
  2. The basic input-output instability results
  3. A state-space instability result
  4. Interconnected systems
Chapter 8. Frequency domain tests
  1. Introduction
  2. General frequency domain criteria
  3. Graphical tests: the scalar case
  4. Graphical tests: the multivariable case
  5. Results using multipliers
  6. Discrete-time systems
  7. Notes and references
Chapter 9.Simple Nonlinear Systems
  1. Introduction
  2. The class of interesting (Q,S,R) triples
  3. General conditions for cyclodissipativeness
  4. Conditions for dissipativeness
  5. Systems with linear dynamics
Chapter 10. Additional results
  1. Relaxed stability tests
  2. Connective stability
  3. An optimal control problem
  4. Dissipation delay
  5. A structure result
Appendix A. Some useful matrix results
  1. A duality result
  2. Matrices with positive principal minors
  3. Quasidominant matrices
  4. M-matrices
  5. Transformations
Bibliography

Index

The author

Peter Moylan is a retired academic in Electrical and Computer Engineering.

If you want to contact him, see the home page for this web site.

This page last updated 21 July 2022.