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Lecture 03 Canonical forms.

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Presentation on theme: "Lecture 03 Canonical forms."— Presentation transcript:

1 Lecture 03 Canonical forms

2 Linear System by Meiling CHEN
Differential equation Dynamical equation or Transfer function Linear System by Meiling CHEN

3 Linear System by Meiling CHEN
Phase-variable canonical form Linear System by Meiling CHEN

4 Linear System by Meiling CHEN
∫ … ＋ Linear System by Meiling CHEN

5 Linear System by Meiling CHEN

6 Linear System by Meiling CHEN
Example 1 Linear System by Meiling CHEN

7 Linear System by Meiling CHEN
controllable canonical form Linear System by Meiling CHEN

8 Linear System by Meiling CHEN
∫ … ＋ Linear System by Meiling CHEN

9 Linear System by Meiling CHEN

10 Linear System by Meiling CHEN
∫ … ＋ + Linear System by Meiling CHEN

11 Linear System by Meiling CHEN
Example 2 Answer 2 Linear System by Meiling CHEN

12 Linear System by Meiling CHEN
observable canonical form Linear System by Meiling CHEN

13 Linear System by Meiling CHEN
∫ + … Linear System by Meiling CHEN

14 Linear System by Meiling CHEN

15 Linear System by Meiling CHEN
Example 3 Linear System by Meiling CHEN

16 Linear System by Meiling CHEN
Remark Linear System by Meiling CHEN

17 Linear System by Meiling CHEN
Diagonal & Jordan canonical form Linear System by Meiling CHEN

18 Linear System by Meiling CHEN
+ Linear System by Meiling CHEN

19 Linear System by Meiling CHEN
Jordan block Linear System by Meiling CHEN

20 Linear System by Meiling CHEN
Example 4 Linear System by Meiling CHEN

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