LMIs in Control/Matrix and LMI Properties and Tools

1. Basic Matrix Theory
2. Notion of Matrix Positivity
3. Matrix Inequalities and LMIs
4. KYP Lemmas
5. Continuous Time
6. Discrete Time
7. Deduced LMI Conditions for H-infinity Index
8. Deduced LMI Conditions for H₂ Index
9. Dissipativity of Systems
10. D-Stabilization
11. H-Stabilization
12. H-2 Norm of the System
13. Algebraic Riccati Equation
14. System Zeros without feedthrough
15. System zeros with feedthrough
16. Negative Imaginary Lemma
17. Small Gain Theorem
18. Tangential Nevanlinna-Pick Interpolation
19. Nevanlinna-Pick Interpolation with Scaling
20. Generalized $H_{2}$ Norm
21. Passivity and Positive Realness
22. Non-expansivity and Bounded Realness
23. Change of Subject
24. Congruence Transformation
25. Finsler's Lemma
26. Young’s Relation (Completion of the Squares)
27. Young’s Relation-Based Properties
28. Schur Stabilizability
29. Variable Reduction Lemma
30. Ellipsoidal inequality
31. Dilation
32. Quadratic Schur Stability
33. D-Stability Rise Time Poles
34. D-Stability Settling Time Poles
35. D-Stability Max Percent Overshoot Poles
36. Iterative Convex Overbounding
37. Strict Projection Lemma
38. Non Strict Projection Lemma
39. Concatenation Of Matrices
40. Dicrete-time Algebraic Riccati Equation
41. Frobenius Norm
42. Dualization Lemma
43. Negative Imaginary System DC Constraint