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Book: Linear matrix inequalities and control theory.

LMIs in Control

Table of contents
Preface

Preliminaries

 * 1) Introduction
 * 2) Notation
 * 3) Fundamentals of Matrix and LMIs
 * 4) Basic Matrix Theory
 * 5) Notion of Matrix Positivity
 * 6) Matrix Inequalities and LMIs
 * 7) Convexity of LMIs
 * 8) Concatenation of LMIs
 * 9) Software for LMIs and Optimization

Properties

 * 1) Properties of LMIs
 * 2) Change of Subject(Variable)
 * 3) Congruence Transformation
 * 4) Young’s Relation (Completion of the Squares)
 * 5) Young’s Relation-Based Properties
 * 6) Special Cases of Young’s Relation
 * 7) Iterative Convex Overbounding
 * 8) Projection Lemma (Matrix Elimination Lemma)
 * 9) Strict Projection Lemma
 * 10) Nonstrict Projection Lemma
 * 11) Reciprocal Projection Lemma
 * 12) Projection Lemma-Based Properties
 * 13) Ellipsoidal Inequality
 * 14) Continuous Time Properties
 * 15) Schur Complement
 * 16) Strict and Nonstrict Schur Complement
 * 17) Schur Complement Lemma-Based Properties
 * 18) Eigenvalue related Problems
 * 19) LMI for Eigenvalue Minimization
 * 20) Eigenvalue Probelm
 * 21) LMI for Generalized Eigenvalue Probelm
 * 22)  LMI for Matrix Norm Minimization
 * 23) LMI for Generalized Eigenvalue Problem
 * 24) LMI for Linear Programming
 * 25) LMI for Feasibility Problem
 * 26) Structured Singular Value
 * 27) LMI for Minimizing Condition Number of Positive Definite Matrix
 * 28) Continuous Quadratic Stability
 * 29) Discrete Time Properties
 * 30) Discrete Time Minimum Gain Lemma
 * 31) Discrete Time Modified Minimum Gain Lemma
 * 32) Finsler’s Lemma
 * 33) Dilation
 * 34) Tangential Nevanlinna Pick
 * 35) Nevanlinna Pick Interpolation with Scaling

Linear Systems

 * 1) Introduction to Linear Systems
 * 2) Kalman-Yakubovich-Popov (KYP) Lemma
 * 3) Continous Time KYP Lemmas
 * 4) Bounded Real Lemma
 * 5) Positive Real Lemma
 * 6) KYP Lemma for QSR Dissipative System
 * 7) KYP Lemma without Feedthrough
 * 8) KYP Lemma with Feedthrough
 * 9) KYP Lemma for Descriptor Systems
 * 10) Discrete Time KYP Lemmas
 * 11) Discrete Time Bounded Real Lemma
 * 12) Discrete Time KYP Lemma for QSR Dissipative System
 * 13) Discrete Time KYP Lemma with Feedthrough
 * 14) Deduced LMI Conditions for H∞ Index
 * 15) H2 Norm of Linear Systems
 * 16) Continuous-Time H2 Norm
 * 17) Discrete-Time H2 Norm
 * 18) Generalized H2 Norm
 * 19) Deduced LMI Conditions for H2 Index
 * 20) Conic Sectors
 * 21) Conic Sector Lemma
 * 22) Exterior Conic Sector Lemma
 * 23) Modified Exterior Conic Sector Lemma
 * 24) Generalized KYP(GKYP) Lemma for conic Sectors
 * 25) Minimum Gain
 * 26) Minimum Gain Lemma
 * 27) Modified Minimum Gain Lemma
 * 28) Discrete-Time Minimum Gain Lemma
 * 29) Discrete-Time Modified Minimum Gain Lemma
 * 30) Negative Imaginary Systems
 * 31) Negative Imaginary Lemma
 * 32) Generalized Negative Imaginary Lemma
 * 33) Algebraic Riccati Inequalities
 * 34) Algebraic Riccati Inequality
 * 35) Discrete-Time Algebraic Riccati Inequality
 * 36) Variable Reduction Lemma
 * 37) System Zeros
 * 38) System Zeros without Feedthrough
 * 39) System Zeros with Feedthrough
 * 40) DC Gain of a Transfer Matrix
 * 41) Dissipativity of Linear Systems
 * 42) Small Gain Theorem
 * 43) Passivity and Positive Realness
 * 44) Non-expansivity and Bounded Realness
 * 45) Stability Theory
 * 46) Lyapunov Inequalities
 * 47) Lyapunov stability
 * 48) Discrete-time Lyapunov Stability
 * 49) Algebric Ricatti Inequalities
 * 50) Discrete-time Algebric Ricatti Inequality
 * 51) Schur Stabilizability
 * 52) Quadratic Stability
 * 53) Continuous-Time Quadratic Stability
 * 54) Discrete-Time Quadratic Stability
 * 55) Quadratic Schur Stability
 * 56) D-Stabilization
 * 57) D-Stability Rise Time Poles
 * 58) D-Stability Settling Time Poles
 * 59) D-Stability Max Percent Overshoot Poles

Non-linear Systems

 * 1) Introduction to Non-linear Systems
 * 2) ...
 * 3) ...
 * 4) ...

Applications

 * 1) LMI for Attitude Control of Nonrotating Missiles
 * 2) Pitch Channel
 * 3) Yaw/ Roll Channel
 * 4) LMI for H2/ H∞ Polytopic controller for Robot Arm
 * 5)  An LMI for the Kalman Filter
 * 6)  H∞ Optimal Model Reduction
 * 7)  An LMI for Multi-Robot Systems
 * 8)  Helicopter Inner Loop LMI
 * 9) Satellite Attitude Control
 * 10) H∞ LMI Satellite Attitude Control
 * 11) H2 LMI Satellite Attitude Control
 * 12) Mixed H2-H∞ LMI Satellite Attitude Control
 * 13) Problem of Space Rendezvous and LMI Approaches
 * 14) LMI for Attitude Control of BTT Missiles, Roll Channel