The theorem of Bohl-Perron on the asimptotic stability of hybrid systems and inverse theorem

P. M. Simonov

Perm State National Research University

Abstract: We consider an abstract hybrid system of two equations with two unknowns: a vector function $x$ that is absolutely continuous on each finite interval $[0,T],$ $T > 0,$ and a sequence of numerical vectors $y.$ The study uses the $W$-method N.V. Azbelev. As a model, a system containing a functional differential equation with respect to $x$ is used, and a difference equation with respect to $y.$ Solutions spaces are studied. For a hybrid system, the Bohl–Perron theorem on asymptotic stability and the converse theorem are obtained.

Keywords: the theorem of Bohl-Perron about the asymptotic stability, hybrid linear system of functional differential equations, method of the model equations, converse theorem.

UDC: 517.962.8

Received: 20.04.2018

DOI: 10.20310/1810-0198-2018-23-124-726-737

Bibliographic databases:

•