| Preface |
| Introduction / 1： |
| Overview |
| A Brief History of LMIs in Control Theory |
| Notes on the Style of the Book |
| Origin of the Book |
| Some Standard Problems Involving LMIs / 2： |
| 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 |
| Some Matrix Problems / 3： |
| 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 |
| Linear Differential Inclusions / 4： |
| Differential Inclusions |
| Some Specific LDIs |
| Nonlinear System Analysis via LDIs |
| Analysis of LDIs: State Properties / 5： |
| Quadratic Stability |
| Invariant Ellipsoids |
| Analysis of LDIs: Input/Output Properties / 6： |
| Input-to-State Properties |
| State-to-Output Properties |
| Input-to-Output Properties |
| State-Feedback Synthesis for LDIs / 7： |
| Static State-Feedback Controllers |
| State Properties |
| Observer-Based Controllers for Nonlinear Systems |
| Lur+1/4 and Multiplier Methods / 8： |
| Analysis of Lur+1/4 Systems |
| Integral Quadratic Constraints |
| Multipliers for Systems with Unknown Parameters |
| Systems with Multiplicative Noise / 9： |
| Analysis of Systems with Multiplicative Noise |
| State-Feedback Synthesis |
| Miscellaneous Problems / 10： |
| 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 |
図書
