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.
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook Linear Matrix Inequalities in System and Control Theory for free.
- Title
- Linear Matrix Inequalities in System and Control Theory
- Author(s)
- Eric Feron, Laurent El Ghaoul, Stephen Boyd, Venkataramanan Balakrishnan
- Published
- 1994-01-01
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 203
- Language
- English
- ISBN-10
- 0898714850
- ISBN-13
- 9780898714852
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Preface Acknowledgments 1 Introduction 1.1 Overview 1.2 A Brief History of LMIs in Control Theory 1.3 Notes on the Style of the Book 1.4 Origin of the Book 2 Some Standard Problems Involving LMIs 2.1 Linear Matrix Inequalities 2.2 Some Standard Problems 2.3 Ellipsoid Algorithm 2.4 Interior-Point Methods 2.5 Strict and Nonstrict LMIs 2.6 Miscellaneous Results on Matrix Inequalities 2.7 Some LMI Problems with Analytic Solutions Notes and References 3 Some Matrix Problems 3.1 Minimizing Condition Number by Scaling 3.2 Minimizing Condition Number of a Positive-Deflnite Matrix 3.3 Minimizing Norm by Scaling 3.4 Rescaling a Matrix Positive-Deflnite 3.5 Matrix Completion Problems 3.6 Quadratic Approximation of a Polytopic Norm 3.7 Ellipsoidal Approximation Notes and References 4 Linear Difierential Inclusions 4.1 Difierential Inclusions 4.2 Some Speciflc LDIs 4.3 Nonlinear System Analysis via LDIs Notes and References 5 Analysis of LDIs: State Properties 5.1 Quadratic Stability 5.2 Invariant Ellipsoids Notes and References 6 Analysis of LDIs: Input/Output Properties 6.1 Input-to-State Properties 6.2 State-to-Output Properties 6.3 Input-to-Output Properties Notes and References 7 State-Feedback Synthesis for LDIs 7.1 Static State-Feedback Controllers 7.2 State Properties 7.3 Input-to-State Properties 7.4 State-to-Output Properties 7.5 Input-to-Output Properties 7.6 Observer-Based Controllers for Nonlinear Systems Notes and References 8 Lur’e and Multiplier Methods 8.1 Analysis of Lur’e Systems 8.2 Integral Quadratic Constraints 8.3 Multipliers for Systems with Unknown Parameters Notes and References 9 Systems with Multiplicative Noise 9.1 Analysis of Systems with Multiplicative Noise 9.2 State-Feedback Synthesis Notes and References 10 Miscellaneous Problems 10.1 Optimization over an A–ne Family of Linear Systems 10.2 Analysis of Systems with LTI Perturbations 10.3 Positive Orthant Stabilizability 10.4 Linear Systems with Delays 10.5 Interpolation Problems 10.6 The Inverse Problem of Optimal Control 10.7 System Realization Problems 10.8 Multi-Criterion LQG 10.9 Nonconvex Multi-Criterion Quadratic Problems Notes and References Notation List of Acronyms Bibliography Index
