Model of time-varying linear systems and Kolmogorov equations

Archives of Control Sciences

Krumov Assen V.¹ 

[1] Higher School of Transport, Sofia, Bulgaria.;

关键词: time-varying;    linear system;    stability;    dynamical systems;    Kolmogorov;    model;   

DOI  :  10.1515/acsc-2015-0013

来源: DOAJ

【 摘 要 】

In the paper an approximate model of time-varying linear systems using a sequence of time-invariant systems is suggested. The conditions for validity of the approximation are proven with a theorem. Examples comparing the numerical solution of the original system and the analytical solution of the model are given. For the system under the consideration a new criterion giving sufficient conditions for robust Lagrange stability is suggested. The criterion is proven with a theorem. Examples are given showing stable and non stable solutions of a time-varying system and the results are compared with the numerical Runge-Kutta solution of the system. In the paper an important application of the described method of solution of linear systems with time-varying coefficients, namely analytical solution of the Kolmogorov equations is shown.

【 授权许可】

Unknown