Krasnosel’skij, M. A.; Mayergoyz, I. D.; Pokrovskij, A. V.; Rachinskij, D. I. Variable states of continuous relay systems. (English. Russian original) Zbl 0819.93006 Russ. Acad. Sci., Dokl., Math. 47, No. 3, 513-517 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 330, No. 4, 427-429 (1993). Hysteresis effects from the operator description point of view are studied and phenomenological models of multidimensional hysteresis nonlinearities are the basic topic of this note. The goal is to remove vague notions about multivaluedness and devices with memory; a mathematical description of hysteresis needs to switch from finite- difference relations to equations with integrals or derivatives. Reviewer: C.Vârsan (Bucureşti) Cited in 1 Review MSC: 93A99 General systems theory 93B28 Operator-theoretic methods 93C10 Nonlinear systems in control theory Keywords:continuous relay systems; modelling; hysteresis effects; operator; nonlinearities PDF BibTeX XML Cite \textit{M. A. Krasnosel'skij} et al., Russ. Acad. Sci., Dokl., Math. 47, No. 3, 1 (1993; Zbl 0819.93006); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 330, No. 4, 427--429 (1993)