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First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.<\/jats:p>","DOI":"10.1177\/0959651820966892","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T07:24:01Z","timestamp":1604301841000},"page":"735-750","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type"],"prefix":"10.1177","volume":"235","author":[{"given":"Xingyu","family":"Zhou","sequence":"first","affiliation":[{"name":"LaFCAS, School of Automation, Nanjing University of Science and Technology, Nanjing, P.R. 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