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On reachable set estimation of delay Markovian jump systems with partially known transition probabilities

Journal Article


Abstract


  • In this paper, the problem of reachable set estimation of discrete-time Markovian jump systems with time-varying delay is addressed. By applying the improved reciprocally convex combination approach to bound the forward difference of double summation and the reciprocally convex combination approach to bound the forward difference of triple summation, a sufficient condition on reachable set estimation is first derived for delay Markovian jump systems with completely known transition probabilities. Then the result is extended to delay Markovian jump systems with partially known transition probabilities. Based on the criterion, a less conservative stability criterion for delay Markovian jump systems is also obtained as a by-product. In order to illustrate the effectiveness and the reduced conservatism of the proposed results, three numerical examples are presented.

Publication Date


  • 2016

Citation


  • Feng, Z., & Zheng, W. X. (2016). On reachable set estimation of delay Markovian jump systems with partially known transition probabilities. Journal of the Franklin Institute, 353(15), 3835-3856. doi:10.1016/j.jfranklin.2016.06.031

Scopus Eid


  • 2-s2.0-84991093324

Web Of Science Accession Number


Start Page


  • 3835

End Page


  • 3856

Volume


  • 353

Issue


  • 15

Abstract


  • In this paper, the problem of reachable set estimation of discrete-time Markovian jump systems with time-varying delay is addressed. By applying the improved reciprocally convex combination approach to bound the forward difference of double summation and the reciprocally convex combination approach to bound the forward difference of triple summation, a sufficient condition on reachable set estimation is first derived for delay Markovian jump systems with completely known transition probabilities. Then the result is extended to delay Markovian jump systems with partially known transition probabilities. Based on the criterion, a less conservative stability criterion for delay Markovian jump systems is also obtained as a by-product. In order to illustrate the effectiveness and the reduced conservatism of the proposed results, three numerical examples are presented.

Publication Date


  • 2016

Citation


  • Feng, Z., & Zheng, W. X. (2016). On reachable set estimation of delay Markovian jump systems with partially known transition probabilities. Journal of the Franklin Institute, 353(15), 3835-3856. doi:10.1016/j.jfranklin.2016.06.031

Scopus Eid


  • 2-s2.0-84991093324

Web Of Science Accession Number


Start Page


  • 3835

End Page


  • 3856

Volume


  • 353

Issue


  • 15