Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 314, Issue 1, Pages 45-66Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2005.03.056
Keywords
interval matrix; Razumikhin method; Brownian motion; Markov chain; m-matrix; exponential stability
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This paper deals with the exponential stability of hybrid stochastic delay interval systems (also known as stochastic delay interval systems with Markovian switching). The known results in this area (see, e.g., [X., Mao, Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Trans. Automat. Control 47 (10) (2002) 1604-1612]) require the time delay to be a constant or a differentiable function and the main reason for such a restriction is due to the analysis of mathematics. The main aim of this paper is to remove this restriction to allow the time delay to be a bounded variable only. The Razumikhin method is developed to cope with the difficulty arisen from the nondifferentiability of the time delay. (c) 2005 Elsevier Inc. All rights reserved.
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