Abstract
This paper begins with a brief summary of the method of convex decomposition, which was first proposed by Kiendl [1, 2] in 1984 and then subsequently developed in cooperation with Ossadnik [3 to 9]. The computer-based method serves as a tool for the robustness analysis of continuous or discrete time linear systems in a state-space representation with uncertain constant or time-varying parameters. For proof of stability purposes, a box-shaped uncertainty domain P is decomposed into ever decreasing sub-boxes until a stability establishing Lyapunov function has been found for each subbox. Exemplified by a case study, it will be demonstrated that the combinatorial explosion can be heavily restrained by strategy elements which have been developed in the meantime. As a result, the method’s practical areas of application may be widely expanded. A fundamental — mathematically obvious but not yet put into practice — extension of the method of convex decomposition is presented in the appendix. It enables broad classes of nonlinearly parameter dependent system matrices to be analysed in the same simple manner as linearly parameter dependent system matrices — without circuitous detours.
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References
H. Kiendl. Stabilitätsnachweis für den Multimodellansatz mit einem Kontinuum von möglichen Parameterwerten. 5. Workshop “Robuste Regelung”, Interlaken 1984. Kurzfassung in Automatisierungstechnik, 33: 192, 1985.
H. Kiendl. Totale Stabilität von linearen Regelungssystemen bei ungenau bekannten Parametern der Regelstrecke. Automatisierungstechnik, 33: 379–386, 1985.
H. Kiendl and H. Ossadnik. Robustheitsanalyse von linearen Systemen mit einem Kontinuum von möglichen Modellparametern. 6. Workshop “Robuste Regelung”, Interlaken 1985. Kurzfassung in Automatisierungstechnik, 34: 170, 1986.
H. Kiendl. Robustheitsanalyse von Regelungssystemen mit der Methode der konvexen Zerlegung. Automatisierungstechnik, 35: 192–202, 1987.
H. Ossadnik. Anwendung der Methode der konvexen Zerlegung zur Robustheitsanalyse des spurgeführten Busses unter Berücksichtigung von Zeitvarianzen. Automatisierungstechnik, 36: 26–31, 1988.
H. Kiendl and H. Ossadnik. Robustness Analysis and Synthesis of Linear Uncertain Systems by the Method of Convex Decomposition. Workshop on Control of Uncertain Systems, Bremen 1989.
H. Ossadnik and H. Kiendl. Robuste quadratische Ljapunov-Funktionen. Automatisierungstechnik, 38: 174–182, 1990.
H. Kiendl and H. Ossadnik. Rechnergestützte Robustheitsanalyse von Regelungssystemen. 6. Internationale Wissenschaftliche Konferenz Anlagenautomatisierung. Wissenschaftliche Berichte der Technischen Hochschule Leipzig, 3: 61–66, 1990.
H. Ossadnik. Robustheitsanalyse linearer Systeme mit der Methode der konvexen Zerlegung. Dissertation, Fortschritt-Berichte VDI, Reihe 8, Nr. 223. VDI-Verlag, Düsseldorf, 1990.
J. Ackermann, H. Z. Hu, and D. Kaesbauer. Robustness Analysis: A Case Study. IEEE Transactions on Automatic Control, 35 (3): 352–356, 1990.
S. Malan, M. Milanese, M. Taragna, and J. Garloff. An Improved Bernstein Algorithm for Robust Stability and Performance Analysis. In Proceedings of the SICICI - Singapore International Conference on Intelligent Control and Instrumentation, February 1992.
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© 1992 Birkhäuser Verlag Basel
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Kiendl, H., Michalske, A. (1992). Robustness Analysis of Linear Control Systems with Uncertain Parameters by the Method of Convex Decomposition. In: Mansour, M., Balemi, S., Truöl, W. (eds) Robustness of Dynamic Systems with Parameter Uncertainties. Monte Verità. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7268-3_19
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DOI: https://doi.org/10.1007/978-3-0348-7268-3_19
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