Krasnosel’skij, M. A.; Rachinskij, D. I. Normal states of vector relay systems. (English. Russian original) Zbl 0818.93004 Russ. Acad. Sci., Dokl., Math. 47, No. 3, 577-580 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 330, No. 5, 556-558 (1993). The systems are nonideal relays with thresholds evolving continuously with vector inputs. The values of the hysteresis nonlinearities are determined by a multiple integral. A theorem on the invariance of the classes of extended state under variable inputs is stated. Reviewer: A.Vaněček (Praha) MSC: 93A99 General systems theory 82D40 Statistical mechanics of magnetic materials 74H99 Dynamical problems in solid mechanics 93B99 Controllability, observability, and system structure Keywords:relay systems; integral systems; nonlinear systems; hysteresis PDFBibTeX XMLCite \textit{M. A. Krasnosel'skij} and \textit{D. I. Rachinskij}, Russ. Acad. Sci., Dokl., Math. 47, No. 3, 1 (1993; Zbl 0818.93004); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 330, No. 5, 556--558 (1993)