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 |
Preface |
Introduction / 1: |
Overview |
A Brief History of LMIs in Control Theory |
Notes on the Style of the Book |
Origin of the Book |