TY - JOUR
N2 - Abstract 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.
L1 - http://www.czasopisma.pan.pl/Content/84367/PDF/4.pdf
L2 - http://www.czasopisma.pan.pl/Content/84367
PY - 2015
IS - No 2
DO - 10.1515/acsc-2015-0013
A1 - Krumov, Assen V.
PB - Committee of Automatic Control and Robotics PAS
T1 - Model of time-varying linear systems and Kolmogorov equations
DA - 2015[2015.01.01 AD - 2015.12.31 AD]
UR - http://www.czasopisma.pan.pl/dlibra/publication/edition/84367
T2 - Archives of Control Sciences
ER -