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Understanding State Transition Matrix in Linear Systems Analysis

Explore the behavior of x(t) and y(t) in linear systems, covering homogeneous and non-homogeneous solutions, properties, convolution, and zero-input/zero-state responses. Learn to find the state transition matrix using Maison’s gain formula and various methods like Cayley-Hamilton Theorem. Discover diagonalization, phase-variable form, and Jordan form in generalized eigenvectors.

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Understanding State Transition Matrix in Linear Systems Analysis

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  1. Linear system 1. Analysis Lesson 6 State transition matrix linear system by Meiling CHEN

  2. The behavior of x(t) et y(t) : • Homogeneous solution of x(t) • Non-homogeneous solution of x(t) linear system by Meiling CHEN

  3. Homogeneous solution State transition matrix linear system by Meiling CHEN

  4. Properties linear system by Meiling CHEN

  5. Non-homogeneous solution Convolution Homogeneous linear system by Meiling CHEN

  6. Zero-input response Zero-state response linear system by Meiling CHEN

  7. Example 1 Ans: linear system by Meiling CHEN

  8. Using Maison’s gain formula linear system by Meiling CHEN

  9. How to find State transition matrix Methode 1: Methode 2: Methode 3: Cayley-Hamilton Theorem linear system by Meiling CHEN

  10. Methode 1: linear system by Meiling CHEN

  11. Methode 2: diagonal matrix linear system by Meiling CHEN

  12. Diagonization linear system by Meiling CHEN

  13. Diagonization linear system by Meiling CHEN

  14. Case 1: depend linear system by Meiling CHEN

  15. In the case of A matrix is phase-variable form and Vandermonde matrix for phase-variable form linear system by Meiling CHEN

  16. Case 1: depend linear system by Meiling CHEN

  17. linear system by Meiling CHEN

  18. Case 3: Jordan form Generalized eigenvectors linear system by Meiling CHEN

  19. Example: linear system by Meiling CHEN

  20. Method 3: linear system by Meiling CHEN

  21. any linear system by Meiling CHEN

  22. Example: linear system by Meiling CHEN

  23. Example: linear system by Meiling CHEN

  24. linear system by Meiling CHEN

  25. linear system by Meiling CHEN

  26. linear system by Meiling CHEN

  27. linear system by Meiling CHEN

  28. linear system by Meiling CHEN

  29. linear system by Meiling CHEN

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