The stability of input-output dynamical systems, Volume 168 (Mathematics in Science and Engineering)

✍ Scribed by Harris (editor)

• Publisher: Academic Press
• Year: 1983
• Tongue: English
• Leaves: 281
• Category: Library

✦ Table of Contents

Front Cover
The Stability of Input–Output Dynamical Systems
Copyright Page
Contents
Preface
Chapter 1. Mathematical Preliminaries
1.1 Introduction
1.2 Basic topological notions
1.3 Topological vector spaces
1.4 Fixed point theorems
1.5 Measures and function spaces
1.6 Dual spaces
1.7 Notes
References
Chapter 2. Riemann Surfaces and the Generalized Principal of the Argument
2.1 Introduction
2.2 Complex integration and Cauchy’s theorem
2.3 Riemann surfaces
2.4 Minimum contours and algebroid Riemann surfaces
2.5 Analytic functions and integration in algebroid Riemann surfaces
2.6 Singular points
2.7 The Generalized Principle of the Argument
References
Chapter 3. Representation of Multipliers
3.1 Introduction
3.2 Representation of multipliers in L2 and L2n
3.3 Convolution algebra M(R+)
3.4 Representation of multipliers in L1 and L1n

3.6 Representation theory in Xp-spaces
References
Chapter 4. Linear Input–Output Stability Theory
4.1 Introduction
4.2 General analytic formulation of stability
4.3 Graphical stability criteria for L2-systems
4.4 Graphical stability criteria for multivariable systems
4.5 Notes
References
Chapter 5. Extended Space Theory in the Study of System operators
5.1 Introduction
5.2 Fundamental results
5.3 Operators in extended spaces
5.4 Well posedness and feedback systems
5.5 Passivity in feedback systems
5.6 Theory of multipliers
5.7 Sectoricity
5.8 Notes
References
Chapter 6. Stability of Nonlinear Multivariable Systems—Circle Criteria
6.1 Introduction
6.2 Small gain theorems
6.3 Intermediate small gain theorem
6.4 Incremental gain theorem
6.5 An M-matrix stability criterion
6.6 System diagonaliszation and design
6.7 Notes
References
Chapter 7. Stability of Nonlinear Multivariable Systems—Passivity Results
7.1 Passivity stability theorems
7.2 Off-axis circle criteria
7.3 Off-axis circle criteria-multiplier factorization
7.4 Multivariable Popov criterion
7.5 Notes
References
Bibliography