Computer analysis of differential systems stability based on linearization and matrix multiplicative criteria

Abstract

This article proposes a method of stability analysis in the sense of Lyapunov for systems of ordinary differential equations. The method is based on stability criteria in the form of necessary and sufficient conditions. The criteria are obtained from matrix multiplicative transformations of difference numerical integration schemes. The form of the criteria entails the possibility of their cyclical software implementation as a cycle based on the number of cofactors. It is mathematically substantiated that the replacement of an infinite matrix product by a finite product, which is necessary in the programming process, preserves the reliability of the stability analysis according to the proposed criteria. We studied the influence of inaccuracy of the difference solution of the system on the reliability of the computer analysis of stability.