# Linear System Theory,2nd edition

• Wilson J. Rugh
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Appropriate for beginning graduate level courses on linear systems, graduate courses introducing linear control, and for self-study.

The basic theory of linear systems is developed in a unified, accessible, and careful manner, with parallel, independent treatment of continuous-time and discrete-time linear systems. Modest mathematical background is assumed, and the technical presentation is explicit and step-by-step. There are many examples to help the reader, and carefully chosen exercises. Includes extensive, annotated citations. The presentation has been repeatedly class tested and refined.

• Clear, careful treatment of basic linear system theory.
• Modular organization for flexibility.
• Compact treatments of polynomial fraction descriptions and the geometric theory.
• Contains results not previously available in text form, including realization theory, noninteracting control, and stabilization results for both continuous-time and discrete-time time-varying linear systems.
• Over 400 exercises.
• Notes section in each chapter provides guides to further study.
• Ten new chapters on discrete-time, time-varying linear systems, the most complete, basic treatment available.
• Theme physical examples throughout the material, plus additional theoretical examples.
• More drill exercises.
• Expanded treatment of the time-invariant case.
• Material on time-varying, reduced-dimension observers.
• Geometric treatment of time-invariant canonical structure theorem.
• Many improvements to the continuous-time presentation.

Preface.

1. Mathematical Notation and Review.

2. State Equation Representation.

3. State Equation Solution.

4. Transition Matrix Properties.

5. Two Important Cases.

6. Internal Stability.

7. Lyapunov Stability Criteria.

9. Controllability and Observability.

10. Realizability.

11. Minimal Realization.

12. Input-Output Stability.

13. Controller and Observer Forms.

14. Linear Feedback.

15. State Observation.

16. Polynomial Fraction Description.

17. Polynomial Fraction Applications.

18. Geometric Theory.

19. Applications of Geometric Theory.

20. Discrete Time: State Equations.

21. Discrete Time: Two Important Cases.

22. Discrete Time: Internal Stability.

23. Discrete Time: Lyapunov Stability Criteria.

24. Discrete Time: Additional Stability Criteria.

25. Discrete Time: Reachability and Observability.

26. Discrete Time: Realization.

27. Discrete Time: Input-Output Stability.

28. Discrete Time: Linear Feedback.

29. Discrete Time: State Observation.

Author Index.

Subject Index.

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