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Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates
Author(s) -
Kao Yonggui,
Yang Tianshu,
Park Ju H.
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3970
Subject(s) - mathematics , exponential stability , jumping , stability (learning theory) , exponential function , markov process , control theory (sociology) , transition rate matrix , exponential growth , type (biology) , jump , square (algebra) , upper and lower bounds , statistical physics , mathematical analysis , computer science , physics , statistics , control (management) , nonlinear system , physiology , ecology , geometry , quantum mechanics , machine learning , artificial intelligence , biology
Summary In this paper, the exponential mean‐square stability of neutral switching Markovian jump systems with generally incomplete transition probabilities is investigated. The model discussed in this paper concludes both deterministic switching signals and Markovian jumping signals. The transition rates of the jumping process are assumed to be partly available, that is, some elements have been exactly known, some have been merely known with lower and upper bounds, and others may have no information to use. Based on the Lyapunov‐Krasovskii functional method, sufficient conditions on the exponential mean‐square stability of the considered system are derived in terms of liner matrix inequalities. A numerical example is provided to show the feasibility and effectiveness of the proposed results.