LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs
Fundamentals of Matrix and LMIs
Fundamentals of Matrix and LMIs
- Basic Matrix Theory
- Notion of Matrix Positivity
- Matrix Inequalities and LMIs
- Convexity of LMIs
- Concatenation of LMIs
Properties of LMIs
- Change of Subject
- Congruence Transformation
- Young’s Relation (Completion of the Squares)
- Projection Lemma (Matrix Elimination Lemma)
- Ellipsoidal inequality
- Continuous Time Properties
- Schur Complement
- Eigenvalue related Problems
- Matrix Norm Minimization
- LMI for Generalized Eigenvalue Problem
- LMI for Linear Programming
- LMI for Feasibility Problem
- Continuous Time/Structured Singular Value
- LMI for Minimizing Condition Number of Positive Definite Matrix
- Continuous time quadratic stability
- Minimizing Norm by Scaling
- Discrete Time Properties
- Finsler’s Lemma
- Dilation
- Tangential Nevanlinna Pick
- Nevanlinna Pick Interpolation with Scaling
- Deduced LMI Conditions for Hinf Index
- Deduced LMI Conditions for H2 Index
- Dissipativity of Systems
- Generalized H2 Norm
- Passivity and Positive Realness
- Non-Expansivity and boundedness Realness
- Variable Reduction Lemma
- D-stability Rise Poles
- D-stability Settling time poles
- D-stability Max Percent Overshoot Poles
- Iterative Convex Overbounding
- Frobenius Norm
- Dualization Lemma
- Submatrix Determinants and Imaginary and Real Parts