Linear matrix inequalities in system and control theory

✍ Scribed by Stephen P Boyd

• Publisher: Society for Industrial and Applied Mathematics
• Year: 1994
• Tongue: English
• Leaves: 206
• Series: SIAM studies in applied mathematics, 15
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Content: 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. Lure and Multiplier Methods. Analysis of Lure 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.