LMIs in Control/Fundamentals of Matrix and LMIs

Fundamentals of Matrix and LMIs

Fundamentals of Matrix and LMIs

1. Basic Matrix Theory
2. Notion of Matrix Positivity
3. Matrix Inequalities and LMIs
4. Convexity of LMIs
5. Concatenation of LMIs

Properties of LMIs

1. Change of Subject(Variable)
2. Congruence Transformation
3. Young’s Relation (Completion of the Squares)
   1. Young’s Relation-Based Properties
   2. Special Cases of Young’s Relation
   3. Iterative Convex Overbounding
4. Projection Lemma (Matrix Elimination Lemma)
   1. Strict Projection Lemma
   2. Nonstrict Projection Lemma
   3. Reciprocal Projection Lemma
   4. Projection Lemma-Based Properties
5. Ellipsoidal Inequality
6. Continuous Time Properties
   1. Schur Complement
      1. Strict and Nonstrict Schur Complement
      2. Schur Complement Lemma-Based Properties
   2. Eigenvalue related Problems
      1. LMI for Eigenvalue Minimization
      2. Eigenvalue Problem
      3. LMI for Generalized Eigenvalue Problem
   3. LMI for Matrix Norm Minimization
   4. LMI for Generalized Eigenvalue Problem
   5. LMI for Linear Programming
   6. LMI for Feasibility Problem
   7. Structured Singular Value
   8. LMI for Minimizing Condition Number of Positive Definite Matrix
   9. Continuous Quadratic Stability
7. Discrete Time Properties
   1. Discrete Time Minimum Gain Lemma
   2. Discrete Time Modified Minimum Gain Lemma
8. Finsler’s Lemma
9. Dilation
10. Tangential Nevanlinna Pick
11. Nevanlinna Pick Interpolation with Scaling