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On the stability of some relay‐type regulation system
Author(s) -
Appell J.,
Pryadko I.N.,
Sadovsky B.N.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800008
Subject(s) - stability theory , stability (learning theory) , relay , type (biology) , control theory (sociology) , mathematics , process (computing) , exponential stability , computer science , physics , thermodynamics , biology , ecology , nonlinear system , control (management) , power (physics) , quantum mechanics , machine learning , artificial intelligence , operating system
This note is concerned with the stability problem for solutions of a system which arises in the mathematical modelling of a temperature regulation device. It is well‐known that, for autonomous systems, a periodic regulation process can be asymptotically stable only if it is stationary. In this paper we consider the case where the “heating” equation is time‐dependent. We show that in this case, under suitable hypotheses, the solution is asymptotically stable, and we also give estimates for approximations of solutions.