{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:21:41Z","timestamp":1787322101879,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2025,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Motivated by the concepts of volumetric controllability score (VCS) and average energy controllability score (AECS) proposed for linear time-invariant systems, we consider the generalization of such concepts to switched linear systems in this paper. The key step of the generalization is to build a similar link between the controllability scores and the optimization objects as in the time-invariant case. Through the link, two families of convex optimization problems, corresponding to the concepts of generalized VCS (GVCS) and generalized AECS (GAECS), respectively, are proposed. Then, we show the uniqueness of the solutions to these problems. These unique solutions are exactly the finite-time controllability scores we want, which provide a quantitative measure of the importance of each state node on controllability during each switching interval. Besides, an algorithm is provided to calculate the GVCS and GAECS based on the projected gradient method. Finally, numerical experiments are presented to verify the effectiveness and superiority of the generalized scores to evaluate the importance of each state node on controllability under a switched network structure.<\/jats:p>","DOI":"10.1137\/24m1686334","type":"journal-article","created":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T07:45:58Z","timestamp":1756799158000},"page":"3139-3166","source":"Crossref","is-referenced-by-count":1,"title":["Finite-Time Controllability Scores of Large-Scale Switched Systems"],"prefix":"10.1137","volume":"63","author":[{"given":"Yao","family":"Mo","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Tongji University, Shanghai, 200092 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9581-8336","authenticated-orcid":true,"given":"Jitao","family":"Sun","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics and Statistics, Nantong University, Nantong, 226019 China, and School of Mathematical Sciences, Tongji University, Shanghai, 200092, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kazuhiro","family":"Sato","sequence":"additional","affiliation":[{"name":"Department of Mathematical Informatics, Graduate School of Information Science and Technology, the University of Tokyo, Japan."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,9,2]]},"reference":[{"key":"ref1","volume-title":"Nonlinear Programming","author":"Bertsekas D. P.","year":"2016","edition":"3"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0946-6"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/22M1482226"},{"key":"ref4","volume-title":"A Course in Robust Control Theory: A Convex Approach","author":"Dullerud G. 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