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Stability of Infinite-dimensional Sampled-data Systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Rebarber, Richard Townley, Stuart |
| Copyright Year | 2003 |
| Abstract | Suppose that a static-state feedback stabilizes a continuous-time linear infinite-dimensional control system. We consider the following question: if we construct a sampled-data controller by applying an idealized sample-andhold process to a continuous-time stabilizing feedback, will this sampled-data controller stabilize the system for all sufficiently small sampling times? Here the state space X and the control space U are Hilbert spaces, the system is of the form ẋ(t) = Ax(t) + Bu(t), where A is the generator of a strongly continuous semigroup on X, and the continuous time feedback is u(t) = Fx(t). The answer to the above question is known to be “yes” if X and U are finitedimensional spaces. In the infinite-dimensional case, if F is not compact, then it is easy to find counterexamples. Therefore, we restrict attention to compact feedback. We show that the answer to the above question is “yes”, if B is a bounded operator from U into X. Moreover, if B is unbounded, we show that the answer “yes” remains correct, provided that the semigroup generated by A is analytic. We use the theory developed for static-state feedback to obtain analogous results for dynamic-output feedback control. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.unl.edu/~rrebarber1/S0002-9947-03-03142-8.pdf |
| Alternate Webpage(s) | http://www.math.unl.edu/~rrebarbe/S0002-9947-03-03142-8.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Block cipher mode of operation Control system Controllers Data system Feedback Hilbert space Sampling (signal processing) Sampling - Surgical action State space |
| Content Type | Text |
| Resource Type | Article |
