{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:36:55Z","timestamp":1740141415994,"version":"3.37.3"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T00:00:00Z","timestamp":1682035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100002338","name":"Ministry of Education of China","doi-asserted-by":"publisher","award":["IRT 16R53"],"award-info":[{"award-number":["IRT 16R53"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,6,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we mainly studied the topological equivalence of linear time-varying (LTV) control system $\\dot{x}\\left ( t\\right )=A(t)x(t)+B(t)u(t)$ defined on an interval $I \\subset \\mathbb{R}^{+}$. After giving a new definition of the topological equivalence, we investigated the local equivalence of LTV control systems under two new hypotheses. These hypotheses were made by the local behavior of Krylov indices (which turned out to be controllability indices for the linear time-invariant (LTI) control systems). It was found out that Krylov indices play an important role in the classification problem of LTV control systems. Compared with our former work on the topological equivalence of LTI control systems, new methods and techniques were taken to deal with new difficulties occurred for LTV control systems.<\/jats:p>","DOI":"10.1093\/imamci\/dnad009","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T11:01:10Z","timestamp":1682334070000},"page":"253-284","source":"Crossref","is-referenced-by-count":0,"title":["Topological equivalence of linear time-varying control systems"],"prefix":"10.1093","volume":"40","author":[{"given":"Jing","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Southwestern University of Finance and Economics , Chengdu 611130 , China"}]},{"given":"Zhixiong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sichuan University , Chengdu 610064 , China"}]}],"member":"286","published-online":{"date-parts":[[2023,4,21]]},"reference":[{"key":"2023061613182926600_ref1","first-page":"427","article-title":"A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems, differ","volume":"1","author":"Ammar Khodja","year":"2009","journal-title":"Equ. 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