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Two cased of hybrid systems are investigated: (i) the impulsive instants and switching instants are synchronous; (ii) the impulsive instants and switching instants are asynchronous. Furthermore, we allow the upper bound of Lyapunov-Razumikhin function with two indefinite derivatives. Then, by using the technique of Lyapunov-Razumikhin, comparison principles combined with the mode-dependent average dwell time (MDADT) and the mode-dependent average impulsive interval (MDAII), we obtain the FTISS property. Finally, we give an example to apply our result and verify its effectiveness.<\/jats:p>","DOI":"10.1177\/09596518251383215","type":"journal-article","created":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T05:50:27Z","timestamp":1763531427000},"page":"77-92","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Finite-time input-to-state stability of time-varying stochastic hybrid time-delay systems"],"prefix":"10.1177","volume":"240","author":[{"given":"Guimin","family":"Xu","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-3394-2977","authenticated-orcid":false,"given":"Meng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan, China"},{"name":"MOE-LCSM, School of Mathematical and Statistics, Hunan Normal University, Changsha, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quanxin","family":"Zhu","sequence":"additional","affiliation":[{"name":"MOE-LCSM, School of Mathematical and Statistics, Hunan Normal University, Changsha, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ding","family":"Kui","sequence":"additional","affiliation":[{"name":"Anhui Polytechnic University, Wuhu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2025,11,18]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"Hybrid dynamical systems: modeling, stability, and robustness","author":"Goebel R","year":"2012","unstructured":"Goebel R, Sanfeice RG, Teel AR. 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