Stabilization of Continuous-Time Markov Jump Linear Systems with Defective Statistics of Modes Transitions

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Gao, Huijun, You, Jia, Shi, Peng, Zhang, Lixian and Zhao, Ye (2011) Stabilization of Continuous-Time Markov Jump Linear Systems with Defective Statistics of Modes Transitions. In: Proceedings of the 18th IFAC World Congress. Bittanti, Sergio, Cenedese, Angelo and Zampieri, Sandro, eds. International Federation of Automatic Control, [Milano, Italy], pp. 8693-8698.

Abstract

This paper concerns the stabilization problem of a class of Markov jump linear system (MJLS) with defective statistics of modes transitions in the continuous-time domain. Differing from the recent separate studies on the so-called uncertain transition probabilities (TPs) and partially unknown TPs, the defective statistics about modes transitions in this study take the two situations into account in a composite way. The scenario is more practicable in that it divides the TPs into three sets: known, uncertain and unknown. The necessary and suffcient conditions for the stability and stabilization of the underlying system are obtained by fully using the properties of the transition rate matrix (TRM) and the convexity of uncertain domains. The monotonicity, in concern of the existence of the admissible stabilizing controller, is observed when the unknown elements become uncertain and the intervals of the uncertain ones become tighter. Numerical examples are provided to verify the theoretical findings.

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Additional Information

The 18th World Congress of the International Federation of Automatic Control (IFAC) was held in Milano, Italy, from Sunday August 28th to Friday September 2nd, 2011

Item type Book Section
URI https://vuir.vu.edu.au/id/eprint/10561
DOI https://doi.org/10.3182/20110828-6-IT-1002.01710
Official URL http://www.ifac-papersonline.net/Detailed/50337.ht...
ISBN 9783902661937
Subjects Historical > Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
Historical > FOR Classification > 0802 Computation Theory and Mathematics
Historical > SEO Classification > 970108 Expanding Knowledge in the Information and Computing Sciences
Keywords ResPubID25058, hybrid systems stability, hybrid systems modeling and control, switched discrete and hybrid systems, transition probability
Citations in Scopus 2 - View on Scopus
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