{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,9]],"date-time":"2023-09-09T05:00:54Z","timestamp":1694235654171},"reference-count":11,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T00:00:00Z","timestamp":1566864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper studies stochastic boundedness of trajectories of a non-vanishing stochastically perturbed stable linear time-invariant system. First, two definitions on stochastic boundedness are presented, then, the boundedness is analyzed via Lyapunov theory. A theorem is proposed, which shows that under a condition on the Lipchitz constant of the perturbation kernel, the trajectories remain stochastically bounded, and the bounds are calculated. Also, the limiting behaviour of the trajectories is studied. At the end, an illustrative example is presented, which shows the effectiveness of the proposed theory.<\/jats:p>","DOI":"10.1093\/imamci\/dnz023","type":"journal-article","created":{"date-parts":[[2019,7,3]],"date-time":"2019-07-03T03:09:54Z","timestamp":1562123394000},"page":"718-729","source":"Crossref","is-referenced-by-count":1,"title":["Stochastic boundedness of state trajectories of stable LTI systems in the presence of non-vanishing stochastic perturbation"],"prefix":"10.1093","volume":"37","author":[{"given":"Peyman","family":"Azodi","sequence":"first","affiliation":[{"name":"School of Electrical and Computer Engineering, Shiraz University, Shiraz 71348-51154, Iran"}]},{"given":"Peyman","family":"Setoodeh","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Shiraz University, Shiraz 71348-51154, Iran"}]},{"given":"Alireza","family":"Khayatian","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Shiraz University, Shiraz 71348-51154, Iran"}]},{"given":"Elham","family":"Jamalinia","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Shiraz University, Shiraz 71348-51154, Iran"}]}],"member":"286","published-online":{"date-parts":[[2019,8,27]]},"reference":[{"key":"2021060109591858200_ref1","volume-title":"Stochastic Differential Equations: Theory and Applications","author":"Arnold","year":"1974"},{"key":"2021060109591858200_ref2","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1109\/IranianCEE.2017.7985135","article-title":"Expectational boundedness of stable LTI systems in the presence of nonvanishing stochastic perturbation","volume-title":"2017 Iranian Conference on Electrical Engineering (ICEE)","author":"Azodi","year":"2017"},{"key":"2021060109591858200_ref3","volume-title":"Linear Stochastic Control Systems","author":"Chen","year":"1995"},{"key":"2021060109591858200_ref4","volume-title":"Real Analysis: Modern Techniques and Their Applications","author":"Folland","year":"2007"},{"key":"2021060109591858200_ref5","volume-title":"Stochastic Differential Equations and Applications","author":"Friedman","year":"1975"},{"key":"2021060109591858200_ref6","volume-title":"Nonlinear Systems","author":"Khalil","year":"2002"},{"key":"2021060109591858200_ref7","volume-title":"Stochastic Stability of Differential Equations","author":"Khasminskii","year":"2013"},{"key":"2021060109591858200_ref8","volume-title":"Stochastic Stability and Control","author":"Kushner","year":"1972"},{"key":"2021060109591858200_ref9","first-page":"1","article-title":"Boundedness and exponential stability of highly nonlinear stochastic differential equations","volume":"143","author":"Liu","year":"2009","journal-title":"Electron. 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