Linear Matrix Inequalties in System and Control Theory

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: Lur'e and Multiplier Methods. Analysis of Lur'e 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.