On almost sure stability conditions of linear switching stochastic differential systems |
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| Institution: | 1. School of Information and Control Engineering, Liaoning Shihua University, Fushun 113001, Liaoning, China;2. Institute of Systems Science, Northeastern University, Shenyang 110819, Liaoning, China;3. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, Liaoning, China;4. School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China;1. Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin 300387, PR China;2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong;3. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China |
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| Abstract: | In modeling practical systems, it can be efficient to apply Poisson process and Wiener process to represent the abrupt changes and the environmental noise, respectively. Therefore, we consider the systems affected by these random processes and investigate their joint effects on stability. In order to apply Lyapunov stability method, we formulate the action of the infinitesimal generator corresponding to such a system. Then, we derive the almost sure stability conditions by using some fundamental convergence theorem. To illustrate the theoretical results, we construct an example to show that it is possible to achieve stabilization by using random perturbations. |
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| Keywords: | Switching systems Stochastic systems Almost sure stability |
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