The document discusses useful transformations for state-space systems, including transforming a system into controllable canonical form and observable canonical form. It also discusses the invariance property of controllability and observability, where these properties remain unchanged under nonsingular state transformations.

1. Digital Control Systems
State-Space Approach II

2. USEFUL TRANSFORMATIONS

3. USEFUL TRANSFORMATIONS

4. USEFUL TRANSFORMATIONS
Controllable Canonical Form:

5. USEFUL TRANSFORMATIONS
Controllable Canonical Form:

6. USEFUL TRANSFORMATIONS
Controllable Canonical Form:

7. USEFUL TRANSFORMATIONS
Controllable Canonical Form:

8. USEFUL TRANSFORMATIONS
Controllable Canonical Form:

9. USEFUL TRANSFORMATIONS
Controllable Canonical Form:

10. USEFUL TRANSFORMATIONS
Controllable Canonical Form:

11. USEFUL TRANSFORMATIONS
Controllable Canonical Form:

12. Controllable Canonical Form:
USEFUL TRANSFORMATIONS

13. USEFUL TRANSFORMATIONS

14. USEFUL TRANSFORMATIONS

15. USEFUL TRANSFORMATIONS

16. USEFUL TRANSFORMATIONS

17. USEFUL TRANSFORMATIONS
Observable Canonical Form:

18. USEFUL TRANSFORMATIONS
Observable Canonical Form:

19. USEFUL TRANSFORMATIONS

20. USEFUL TRANSFORMATIONS

21. USEFUL TRANSFORMATIONS

22. USEFUL TRANSFORMATIONS

23. USEFUL TRANSFORMATIONS

24. USEFUL TRANSFORMATIONS

25. USEFUL TRANSFORMATIONS

26. USEFUL TRANSFORMATIONS

27. USEFUL TRANSFORMATIONS

28. USEFUL TRANSFORMATIONS

29. USEFUL TRANSFORMATIONS

30. USEFUL TRANSFORMATIONS

31. INVARIANCE PROPERTY OF CONTROLLABILITY AND
OBSERVABILITY

32. INVARIANCE PROPERTY OF CONTROLLABILITY
AND OBSERVABILITY