Linear Matrix Inequalties in System and Control Theory
Will be published approx. on 31. December 1994
Book
Paperback/Softback
203 pages
978-0-89871-485-2 (ISBN)
Description
In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.
Special Features:
The book identifies a handful of standard optimization problems that are general (a wide variety of problems from system and control theory can be reduced to them) as well as specific (specialized numerical algorithms can be devised for them).
Catalogues a diverse list of problems in system and control theory that can be reduced to the standard optimization problems.
Problems considered are analysis and state feedback design for uncertain systems, matrix analysis problems, and many others.
Most of the the book is accessible to anyone with a basic mathematics background, e.g., linear algebra and differential equations.
Special Features:
The book identifies a handful of standard optimization problems that are general (a wide variety of problems from system and control theory can be reduced to them) as well as specific (specialized numerical algorithms can be devised for them).
Catalogues a diverse list of problems in system and control theory that can be reduced to the standard optimization problems.
Problems considered are analysis and state feedback design for uncertain systems, matrix analysis problems, and many others.
Most of the the book is accessible to anyone with a basic mathematics background, e.g., linear algebra and differential equations.
More details
Series
Edition
Revised edition
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 259 mm
Width: 179 mm
Thickness: 17 mm
Weight
444 gr
ISBN-13
978-0-89871-485-2 (9780898714852)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
Preface
Chapter 1: Introduction. Overview
A Brief History of LMIs in Control Theory
Notes on the Style of the Book
Origin of the Book
Chapter 2: Some Standard Problems Involving LMIs. Linear Matrix Inequalities
Some Standard Problems
Ellipsoid Algorithm
Interior-Point Methods
Strict and Nonstrict LMIs
Miscellaneous Results on Matrix Inequalities
Some LMI Problems with Analytic Solutions
Chapter 3: Some Matrix Problems. Minimizing Condition Number by Scaling
Minimizing Condition Number of a Positive-Definite Matrix
Minimizing Norm by Scaling
Rescaling a Matrix Positive-Definite
Matrix Completion Problems
Quadratic Approximation of a Polytopic Norm
Ellipsoidal Approximation
Chapter 4: Linear Differential Inclusions. Differential Inclusions
Some Specific LDIs
Nonlinear System Analysis via LDIs
Chapter 5: Analysis of LDIs: State Properties. Quadratic Stability
Invariant Ellipsoids
Chapter 6: Analysis of LDIs: Input/Output Properties. Input-to-State Properties
State-to-Output Properties
Input-to-Output Properties
Chapter 7: State-Feedback Synthesis for LDIs. Static State-Feedback Controllers
State Properties
Input-to-State Properties
State-to-Output Properties
Input-to-Output Properties
Observer-Based Controllers for Nonlinear Systems
Chapter 8: Lur'e and Multiplier Methods. Analysis of Lur'e Systems
Integral Quadratic Constraints
Multipliers for Systems with Unknown Parameters
Chapter 9: Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise
State-Feedback Synthesis
Chapter 10: Miscellaneous Problems. Optimization over an Affine Family of Linear Systems
Analysis of Systems with LTI Perturbations
Positive Orthant Stabilizability
Linear Systems with Delays
Interpolation Problems
The Inverse Problem of Optimal Control
System Realization Problems
Multi-Criterion LQG
Nonconvex Multi-Criterion Quadratic Problems
Notation
List of Acronyms
Bibliography
Index.
Chapter 1: Introduction. Overview
A Brief History of LMIs in Control Theory
Notes on the Style of the Book
Origin of the Book
Chapter 2: Some Standard Problems Involving LMIs. Linear Matrix Inequalities
Some Standard Problems
Ellipsoid Algorithm
Interior-Point Methods
Strict and Nonstrict LMIs
Miscellaneous Results on Matrix Inequalities
Some LMI Problems with Analytic Solutions
Chapter 3: Some Matrix Problems. Minimizing Condition Number by Scaling
Minimizing Condition Number of a Positive-Definite Matrix
Minimizing Norm by Scaling
Rescaling a Matrix Positive-Definite
Matrix Completion Problems
Quadratic Approximation of a Polytopic Norm
Ellipsoidal Approximation
Chapter 4: Linear Differential Inclusions. Differential Inclusions
Some Specific LDIs
Nonlinear System Analysis via LDIs
Chapter 5: Analysis of LDIs: State Properties. Quadratic Stability
Invariant Ellipsoids
Chapter 6: Analysis of LDIs: Input/Output Properties. Input-to-State Properties
State-to-Output Properties
Input-to-Output Properties
Chapter 7: State-Feedback Synthesis for LDIs. Static State-Feedback Controllers
State Properties
Input-to-State Properties
State-to-Output Properties
Input-to-Output Properties
Observer-Based Controllers for Nonlinear Systems
Chapter 8: Lur'e and Multiplier Methods. Analysis of Lur'e Systems
Integral Quadratic Constraints
Multipliers for Systems with Unknown Parameters
Chapter 9: Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise
State-Feedback Synthesis
Chapter 10: Miscellaneous Problems. Optimization over an Affine Family of Linear Systems
Analysis of Systems with LTI Perturbations
Positive Orthant Stabilizability
Linear Systems with Delays
Interpolation Problems
The Inverse Problem of Optimal Control
System Realization Problems
Multi-Criterion LQG
Nonconvex Multi-Criterion Quadratic Problems
Notation
List of Acronyms
Bibliography
Index.