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

Gao, Huijun and You, Jia and Shi, Peng and 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 and Cenedese, Angelo and Zampieri, Sandro, eds. International Federation of Automatic Control, [Milano, Italy], pp. 8693-8698.

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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.

Item Type: Book Section
ISBN: 9783902661937
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

Uncontrolled Keywords: ResPubID25058, hybrid systems stability, hybrid systems modeling and control, switched discrete and hybrid systems, transition probability
Subjects: Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
FOR Classification > 0802 Computation Theory and Mathematics
SEO Classification > 970108 Expanding Knowledge in the Information and Computing Sciences
Related URLs:
Depositing User: VUIR
Date Deposited: 19 Jan 2014 00:14
Last Modified: 19 Jan 2014 00:14
URI: http://vuir.vu.edu.au/id/eprint/10561
DOI: 10.3182/20110828-6-IT-1002.01710
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