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Linear Systems

1. Introduction to Linear Systems
2. Kalman-Yakubovich-Popov (KYP) Lemma
   1. Continuous Time KYP Lemmas
      1. Bounded Real Lemma
      2. Positive Real Lemma
      3. KYP Lemma for QSR Dissipative System
      4. KYP Lemma without Feedthrough
      5. KYP Lemma with Feedthrough
      6. KYP Lemma for Descriptor Systems
   2. Discrete Time KYP Lemmas
      1. Discrete Time Bounded Real Lemma
      2. Discrete Time KYP Lemma for QSR Dissipative System
      3. Discrete Time KYP Lemma with Feedthrough
   3. Deduced LMI Conditions for H∞ Index
3. H2 Norm of Linear Systems
   1. Continuous-Time H2 Norm
   2. Discrete-Time H2 Norm
   3. Generalized H2 Norm
   4. Deduced LMI Conditions for H2 Index
4. Conic Sectors
   1. Conic Sector Lemma
   2. Exterior Conic Sector Lemma
   3. /Modified Exterior Conic Sector Lemma
   4. Generalized KYP(GKYP) Lemma for conic Sectors/
5. Minimum Gain
   1. Minimum Gain Lemma
   2. Modified Minimum Gain Lemma
   3. Discrete-Time Minimum Gain Lemma
   4. Discrete-Time Modified Minimum Gain Lemma
6. Negative Imaginary Systems
   1. Negative Imaginary Lemma
   2. Generalized Negative Imaginary Lemma
7. Algebraic Riccati Inequalities
   1. Algebraic Riccati Inequality
   2. Discrete-Time Algebraic Riccati Inequality
   3. Variable Reduction Lemma
8. System Zeros
   1. System Zeros without Feedthrough
   2. System Zeros with Feedthrough
9. DC Gain of a Transfer Matrix
10. Dissipativity of Linear Systems
11. Small Gain Theorem
12. Passivity and Positive Realness
13. Non-expansivity and Bounded Realness
14. Stability Theory
    1. Lyapunov Inequalities
       1. Lyapunov stability
       2. Discrete-time Lyapunov Stability
    2. Algebric Ricatti Inequalities
    3. Discrete-time Algebric Ricatti Inequality
    4. Schur Stabilizability
    5. Quadratic Stability
       1. Continuous-Time Quadratic Stability
       2. Discrete-Time Quadratic Stability
       3. Quadratic Schur Stability
    6. D-Stabilization
       1. D-Stability Rise Time Poles
       2. D-Stability Settling Time Poles
       3. D-Stability Max Percent Overshoot Poles