Linear matrix inequalities and control theory/pages/Fundamentals of Matrix and LMIs

Fundamentals of Matrix and LMIs

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