SIAM Homepage | Search Catalog | New Books | Author Index | Series Index | Title Index | View My Shopping Cart



The catalog and shopping cart are hosted for SIAM by EasyCart. Your transaction is secure. If you have any questions about your order, contact siambooks@siam.org.

Purchase Now!

Linear Matrix Inequalities in System and Control Theory

Stephen Boyd, Laurent El Ghaoui, Eric Feron, and Venkataramanan Balakrishnan



Studies in Applied Mathematics 15

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.

Audience

This book is primarily intended for researchers in system and control theory; both the beginner and the advanced researcher will find the book useful.

Researchers in convex optimization will find this book a source of optimization problems for which algorithms need to be devised. A background in linear algebra, elementary analysis, and exposure to differential equations and system and control theory is recommended.

Contents

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: Luré and Multiplier Methods. Analysis of Luré 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.

Royalties from the sale of this book are contributed to the SIAM Student Travel Fund.

1994 / ix + 193 pages / Softcover / ISBN-13: 978-0-898714-85-2 / ISBN-10: 0-89871-485-0 /
List Price $71.50 / SIAM Member Price $50.05 / Order Code AM15
Price
Quantity desired
   



Search our catalog for:

Shopping cart provided by: EasyCart.com
Select quantity and list or member price and then click the "Click to Order" button to add books to your shopping cart.
Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)