Necessary and Sufi cient Condition for Mean-Square Stability of Linear Stochastic System with Distributed Parameter

Journal of South China University of Technology (Natural Science Edition) ›› 2005, Vol. 33 ›› Issue (5): 15-18.

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Necessary and Sufi cient Condition for Mean-Square Stability of Linear Stochastic System with Distributed Parameter

Song Ya-nan¹ Deng Fei-qi² Luo Qi³ Yang Yi-min¹

1.College of Automation,Guangdong Univ.of Tech.,Guangzhou 510090,Guangdong,China;2.College of Automation Science and Engineering,South China Univ.of Tech.,Guan gzhou 510640,Guan gdong,China;3.College of Science,Wuhan Univ.of Science and Tech.,Wuhan 430081,Hubei,China

Received:2003-10-13 Online:2005-05-25 Published:2005-05-25
Contact: Song Ya-nan(born in 1976)，female，lecturer，Ph． D．，mainly researches on optimization an d control of complex large-scale systems． E-mail:syn01@ 126.com
About author:Song Ya-nan(born in 1976)，female，lecturer，Ph． D．，mainly researches on optimization an d control of complex large-scale systems．
Supported by:
Supported by the National Natural Sc ience Foundation of China(69874015,69934030)and Guangdong Provincial Natural Science Foundation(011629)

Abstract

Abstract:

On the basis of the new mathematical description of the linear stochastic system with distributed pa-rameter,the corresponding definition of mean-square stability is given.Moreover,by transferring partial dife-rential equ ations into ordinary diferential equations an d considering the boundary condition an d Divergence Theolea-the conditions for the stab ility of partial diferential equ ations aTe presented,which aTe based on the stable
conditions of ordinary diferential equ ations.Thus,the necessary an d suficient condition for the mean.square stability of the linear stochastic system with distributed parameter is obtaindd.Simulations are finally presented to verify the correctness of this research.

Key words: stochastic system, distributed parameter, mean-square stability, ItÔ, formula

Song Ya-nan Deng Fei-qi Luo Qi Yang Yi-min. Necessary and Sufi cient Condition for Mean-Square Stability of Linear Stochastic System with Distributed Parameter[J]. Journal of South China University of Technology (Natural Science Edition), 2005, 33(5): 15-18.

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Necessary and Sufi cient Condition for Mean-Square Stability of Linear Stochastic System with Distributed Parameter

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