TY - JOUR

T1 - Systems with Partially Freezed Components

AU - Pilyugin, S. Yu.

N1 - Funding Information: This research was supported by the RFBR (project 18-01-00230A).

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We study a particular class of switching systems called systems with partially freezed components. Fix an autonomous system of differential equations and consider a family of systems obtained from it by replacing some of components of the right-hand side by zeros (thus, “freezing” some components of a solution). We obtain the flow of a system with partially freezed components by fixing a sequence of switching times and of the corresponding sets of “active” components (i.e., the components that are not “freezed”). Such a sequence is called a freezing sequence. Systems with partially freezed components appear, for example, in the study of generalized Turing machines. In this paper, we are mostly interested in stability properties of such systems; our main goal is to relate such properties to properties of the generating system and freezing sequences.

AB - We study a particular class of switching systems called systems with partially freezed components. Fix an autonomous system of differential equations and consider a family of systems obtained from it by replacing some of components of the right-hand side by zeros (thus, “freezing” some components of a solution). We obtain the flow of a system with partially freezed components by fixing a sequence of switching times and of the corresponding sets of “active” components (i.e., the components that are not “freezed”). Such a sequence is called a freezing sequence. Systems with partially freezed components appear, for example, in the study of generalized Turing machines. In this paper, we are mostly interested in stability properties of such systems; our main goal is to relate such properties to properties of the generating system and freezing sequences.

KW - stability

KW - Switching systems

KW - systems with freezed components

UR - http://www.scopus.com/inward/record.url?scp=85049589144&partnerID=8YFLogxK

U2 - 10.1134/S1995080218050116

DO - 10.1134/S1995080218050116

M3 - Article

VL - 39

SP - 707

EP - 712

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 5

ER -