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The results for the latter problem are a small-gain condition and a formula of Lyapunov functions which can be constructed for interconnections whenever the small-gain condition holds. It is demonstrated that for interconnections of partial differential equations, the choice of a right state and input spaces is crucial, in particular for iISS subsystems which are not ISS. As illustrative examples, stability of two highly nonlinear reaction-diffusion systems is established by the proposed small-gain criterion.<\/jats:p>","DOI":"10.1137\/14097269x","type":"journal-article","created":{"date-parts":[[2015,12,2]],"date-time":"2015-12-02T14:16:20Z","timestamp":1449065780000},"page":"3364-3382","source":"Crossref","is-referenced-by-count":67,"title":["Construction of Lyapunov Functions for Interconnected Parabolic Systems: An iISS Approach"],"prefix":"10.1137","volume":"53","author":[{"given":"Andrii","family":"Mironchenko","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hiroshi","family":"Ito","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,11,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2006.08.003"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/9.863594"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1974.1100617"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"T. 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