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 polynomialtime 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; InteriorPoint 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 PositiveDefinite Matrix; Minimizing Norm by Scaling; Rescaling a Matrix PositiveDefinite; 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. InputtoState Properties; StatetoOutput Properties; InputtoOutput Properties; Chapter 7: StateFeedback Synthesis for LDIs. Static StateFeedback Controllers; State Properties; InputtoState Properties; StatetoOutput Properties; InputtoOutput Properties; ObserverBased 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; StateFeedback 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; MultiCriterion LQG; Nonconvex MultiCriterion 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 / ISBN13: 9780898714852 / ISBN10: 0898714850 / List Price $71.50 / SIAM Member Price $50.05 / Order Code AM15
