Linear system theory. – 2a edición
Intended for use in a second course in linear systems theory, this text carefully and rigorously develops core material in the theory of time-varying linear systems. Assuming that you have a modest background in linear and matrix algebra, Laplace and z-transforms, and elementary differential equations, you’ll find the presentation to be relatively self-contained. (Although a prior course in signals and systems would be helpful, it is not required.) The text develops continuous-time and discrete-time concepts and methodologies independently and in parallel.
The frequent specialization to the time-invariant case allows the author to maximize clarity and accessibility of the theory while avoiding unenlightening technicalities. The text also presents material that is more often found in introductory control systems courses (e.g., controllability and observability, Lyapunov stability, and linear feedback and state observation). Of particular note are the chapters on geometric theory and applications, which give interpretation and insight into key systems’ theoretical ideas and results. The text also offers over 400 exercises of varying difficulty as an aid to the reader. Overall, this is an excellent text for graduate or advanced undergraduate students as well as a superb reference source.
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.
8. Additional stability criteria.
9. Controllability and observability.
11. Minimal realization.
12. Input-Output stability.
13. Controller and observer forms.
14. Linear feedback.
15. State observation.
16. Polynomial fraction descrption.
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 citeria.
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.
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