Linear Matrix Inequalities in System and Control Theory

The authors reduce a variety of problems in system / control theory to a handful of convex and quasiconvex optimization problems.

Stephen Boyd (Author), Laurent El Ghaoul (Author), Eric Feron (Author), Venkataramanan Balakrishnan (Author)

9780898714852, Society for Industrial and Applied Mathematics

Paperback / softback, published 1 January 1987

203 pages
25.5 x 18 x 1.5 cm, 0.443 kg

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.

Preface
1. Introduction
Overview
A Brief History of LMIs in Control Theory
Notes on the Style of the Book
Origin of the Book
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
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
4. Linear Differential Inclusions. Differential Inclusions
Some Specific LDIs
Nonlinear System Analysis via LDIs
5. Analysis of LDIs: State Properties. Quadratic Stability
Invariant Ellipsoids
6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties
State-to-Output Properties
Input-to-Output Properties
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
8. Luré and Multiplier Methods. Analysis of Luré Systems
Integral Quadratic Constraints
Multipliers for Systems with Unknown Parameters
9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise
State-Feedback Synthesis
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.

Subject Areas: Numerical analysis [PBKS]