{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:25:37Z","timestamp":1787322337087,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>In the analysis of large-scale interconnected systems, small-gain conditions may be used to derive stability properties of the overall system. This paper investigates the question of how large several gains may be chosen while still satisfying a small-gain condition, if a subset of the gains is fixed. In particular, the cases of summation of linear gains and maximization of gains lead to computable solutions. As an application, we consider the interconnection of a large-scale system with a communication network to be designed. To this end a small-gain theorem in the context of hybrid systems for the interconnection of input-to-state stable and globally pre-stable (pre-GS) subsystems is derived. The pre-GS subsystems model data channels. The construction methods then give gain bounds for the data channels guaranteeing stability of the overall system.<\/jats:p>","DOI":"10.1137\/130924755","type":"journal-article","created":{"date-parts":[[2015,1,22]],"date-time":"2015-01-22T12:10:50Z","timestamp":1421928650000},"page":"262-286","source":"Crossref","is-referenced-by-count":10,"title":["On Maximal Gains Guaranteeing a Small-Gain Condition"],"prefix":"10.1137","volume":"53","author":[{"given":"Roman","family":"Geiselhart","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabian","family":"Wirth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,1,22]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"A. Berman and R. J. Plemmons,\n                      Nonnegative Matrices in the Mathematical Sciences\n                      , Classics Appl. 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Gru\u0308ne,\n                      Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization\n                      , Lecture Notes in Math. 1783, Springer-Verlag, Berlin, 2002.","DOI":"10.1007\/b83677"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2042352"},{"key":"atypb16","first-page":"119","author":"Hinrichsen D.","year":"1990","journal-title":"Basel"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2009.2028980"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(96)00051-9"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211469"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"I. Karafyllis and Z.P. Jiang,\n                      Stability and stabilization of nonlinear systems\n                      , Comm. Control Engrg. 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Ru\u0308ffer,\n                      Monotone Dynamical Systems, Graphs, and Stability of Large-Scale Interconnected Systems\n                      , Ph.D. thesis, Universita\u0308t Bremen, Bremen, Germany, 2007."},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/s11117-009-0016-5"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2048053"},{"key":"atypb31","first-page":"111","volume":"2","author":"Sanfelice R.","year":"2012","journal-title":"J. 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