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LMIs in system and stability Theory

  1. Lyapunov Inequalities
    1. Continuous- time Lyapunov Stability
    2. Discrete-time Lyapunov Stability
    3. Generalized Lyapunov Stability
  2. Bounded Real Lemma and Hinf Norm
    1. Continuous - time Bounded Real Lemma
    2. Discrete - time Bounded Real Lemma
  3. H2 Norm
    1. Continuous- time H2 Norm
    2. Discrete - time H2 Norm
  4. Generalized H2 Norm
  5. Peak-to-Peak Norm
  6. Kalman-Yakubovich-Popov(KYP) Lemma
    1. KYP Lemma for QSR Dissipative Systems
    2. Discrete-Time KYP Lemma for QSR Dissipative Systems
    3. KYP Lemma Without Feedthrough
    4. KYP Lemma with Feedthrough
    5. Discrete-Time KYP Lemma With Feedthrough
    6. KYP Lemma for Descriptor systems
  7. Conic Sectors
    1. Conic Sector Lemma
    2. Exterior Conic Sector Lemma
    3. Modified Exterior Conic Sector Lemma
    4. Generalized KYP Lemma for Conic Sectors
  8. Minimum Gain
    1. Minimum Gain Lemma
    2. Modified Minimum Gain Lemma
    3. Discrete-Time Minimum Gain Lemma
    4. Discrete-Time Modified Minimum Gain Lemma
  9. Negative Imaginary Systems
    1. Negative Imaginary Lemma
    2. Discrete-time Negative Imaginary Lemma
    3. Generalized Negative Imaginary Lemma
  10. Algebraic Riccati Inequalities
    1. Discrete-time Algebraic Riccati Inequalities
  11. Stabilizability
    1. Continuous-time Stabilizability
    2. Discrete-time Stabilizability
  12. Detectability
    1. Continuous-time Detectability
    2. Discrete-time Detectability
  13. Static Output Feedback Stabilizability
    1. Continuous-time Static Output Feedback Stabilizability
    2. Discrete-time Static Output Feedback Stabilizability
  14. Strong Stabilizability
    1. Continuous-time strong stabilizability
    2. Discrete-time strong stabilizability
  15. System Zeros
    1. System Zeros without Feedthrough
    2. System Zeros with Feedthrough
  16. D-Stability
    1. Conic Sector Region Stability via the Dilation Lemma
    2. alpha-Region via the Dilation Lemma
    3. Circular Region Stability via the Dilation Lemma
    4. DC Gain of a Transfer Matrix
    5. Kharitonov-Bernstein-Haddad(KBH) Theorem
  17. D-Admissibility
    1. General LMI Region D-Admissibility
    2. Circular Region D-Admissibility
  18. Quadratic Stability
    1. Continuous-time Quadratic Stability
    2. Discrete-time Quadratic Stability
  19. Stability of Time Delay Systems
    1. Delay-Independent Condition
    2. Delay-Dependent Condition
  20. mu-Analysis
  21. Static Output Feedback Algebraic Loop
  22. Continuous Time
    1. Time-Delay Systems
      1. Delay Dependent Time-Delay Stabilization
      2. Delay Independent Time-Delay Stabilization
    2. Parametric, Norm-Bounded Uncertain System Quadratic Stability
    3. Stability of Structured, Norm-Bounded Uncertainty
    4. Stability under Arbitrary Switching
    5. Quadratic Stability Margins
    6. Stability of Linear Delayed Differential Equations
    7. H infinity Norm for Affine Parametric Varying Systems
    8. Entropy Bond for Affine Parametric Varying Systems
    9. Dissipativity of Affine Parametric Varying Systems
    10. Hankel Norm of Affine Parameter Varying Systems
    11. Positive Orthant Stabilizability
    12. LMI For Stabilization Condition for Systems With Unsymmetrical Saturated Control
    13. LMI Condition For Exponential Stability of Linear Systems With Interval Time-Varying Delays
    14. Polytopic Quadratic Stability
    15. Interval Quadratic Stability
    16. Optimization Over Affine Family of Linear Systems
    17. Hurwitz Stabilizability
    18. Quadratic Hurwitz Stabilization for Polytopic Systems
    19. Output Energy Bound for Autonomous LTI Systems
    20. Transient State Bound for Non-Autonomous LTI Systems
    21. Transient Impulse Response Bound for Non-Autonomous LTI systems
  1. Discrete-time
    1. D-stability
      1. Controller D-Stability
      2. Observer D-stability
    2. Discrete-Time Lyapunov Stability
    3. LMI for Schur Stabilization
    4. L2-Gain of Systems with Multiplicative noise
    5. Discrete-Time Quadratic Stability
    6. Output Energy Bound for Discrete-Time Autonomous LTI Systems
    7. Transient Bound for Discrete-Time Non-Autonomous LTI Systems
    8. Discrete-Time Transient Impulse Response Bound
  1. Lure's System
    1. Stability Of Lure's System
    2. L2 Gain of Lure's Systems
    3. Output Energy Bound for Lure's Systems
  2. Stability of Quadratic Constrained Systems
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