1. linear system by Meiling CHEN1 Lesson 6 State transition matrix Linear system 1. Analysis

2. linear system by Meiling CHEN2 1.Homogeneous solution of x(t) 2.Non-homogeneous solution of x(t) The behavior of x(t) et y(t) :

3. linear system by Meiling CHEN3 Homogeneous solution State transition matrix

4. linear system by Meiling CHEN4 Properties

5. linear system by Meiling CHEN5 Non-homogeneous solution Convolution Homogeneous

6. linear system by Meiling CHEN6 Zero-input responseZero-state response

7. linear system by Meiling CHEN7 Example 1 Ans:

8. linear system by Meiling CHEN8 Using Maison’s gain formula

9. linear system by Meiling CHEN9 How to findState transition matrix Methode 1: Methode 3: Cayley-Hamilton Theorem Methode 2:

10. linear system by Meiling CHEN10 Methode 1:

11. linear system by Meiling CHEN11 Methode 2: diagonal matrix

12. linear system by Meiling CHEN12 Diagonization

13. linear system by Meiling CHEN13 Diagonization

14. linear system by Meiling CHEN14 Case 1: depend

15. linear system by Meiling CHEN15 In the case of A matrix is phase-variable form and Vandermonde matrix for phase-variable form

16. linear system by Meiling CHEN16 Case 1: depend

17. linear system by Meiling CHEN17

18. linear system by Meiling CHEN18 Case 3:Jordan form Generalized eigenvectors

19. linear system by Meiling CHEN19 Example:

20. linear system by Meiling CHEN20 Method 3:

21. linear system by Meiling CHEN21 any

22. linear system by Meiling CHEN22 Example:

23. linear system by Meiling CHEN23 Example:

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