Time-domain boundedness of noise-to-state exponentially stable systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 105.

In this paper we prove the time-domain boundedness for noise-to-state exponentially stable systems, and further make an estimation of its lower bound function, which allows to answer the question that how long the solution of a stochastic noise-to-state exponentially stable system stays in the domain of attraction and what happens with it if it escapes from this region for a while. The results will complement the probability-domain boundedness of noise-to-state exponentially stable systems, and provide a new insight into noise-to-state exponential stability.

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DOI : 10.1051/cocv/2020037
Classification : 93E15, 60H10
Mots-clés : Noise-to-state exponential stability, stochastic differential equation, persistent noise, loop, time-domain boundedness 
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     author = {Fang, Zhou and Gao, Chuanhou},
     title = {Time-domain boundedness of noise-to-state exponentially stable systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
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     zbl = {1461.93531},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2020037/}
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Fang, Zhou; Gao, Chuanhou. Time-domain boundedness of noise-to-state exponentially stable systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 105. doi : 10.1051/cocv/2020037. http://www.numdam.org/articles/10.1051/cocv/2020037/

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This work was supported by the National Nature Science Foundation of China under Grant No. 11671418, and the Zhejiang Provincial Natural Science Foundation of China under Grant No. LZ20A010002.