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Razumikhin method and exponential stability of hybrid stochastic delay interval systems |
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| Authors: | Xuerong Mao James Lam Huijun Gao |
| Affiliation: | a Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UK b Department of Mechanical Engineering, University of Hong Kong, Hong Kong c Department of Automation, Nanjing University of Science and Technology, Nanjing 210094, PR China d Inertial Navigation Centre, Harbin Institute of Technology, Harbin 150001, PR China |
| Abstract: | 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. |
| Keywords: | Interval matrix Razumikhin method Brownian motion Markov chain M-matrix Exponential stability |
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