Comparison of direct and perturbation approaches to analysis of infinite-dimensional feedback control systems

• Autorzy: Grabowski Piotr

Identyfikatory

DOI

10.34768/amcs-2021-0014

• Języki publikacji: EN

Abstrakty

EN

For general boundary control systems in factor form some necessary and sufficient conditions for generation of an analytic exponentially stable semigroup are proposed in both direct and perturbation forms for comparison. The direct approach is applicable to operators with the numerical range satisfying certain additional conditions. In particular, it applies to operators similar to convexoids and therefore it generalizes previous results known for hyponormal operators. The perturbation result (indirect approach) is derived and formulated as an exponential stability robustness result using the frequence-domain considerations. It is expressed in terms of some estimates of the resolvent growth over the open right complex half-plane and compared with some recent results. The analysis is illustrated in detail with examples of an unloaded and loaded electric RC-transmission line with proportional negative feedback.

Słowa kluczowe

EN

perturbation; semigroups; systems in factor form; spectral operators

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2021
• Tom: Vol. 31, no. 2
• Strony: 195--218
• Opis fizyczny: Bibliogr. 43 poz., rys., tab.

Twórcy

autor

Grabowski Piotr

• Institute of Control Engineering and Robotics, AGH University of Science and Technology, Al. Mickiewicza 30/B1, 30-059 Kraków, Poland

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).