The method of Lyapunov functions for systems of linear difference equations with almost periodic coefficients
In their article [Mat. Zametki 52, No. 6, 10-14 (1992; Zbl 0798.34056)], \textit{S. M. Dobrovol'skij}, \textit{A. S. Kotyurgina} and \textit{R. K. Romanovskij} established a test exponential stability of the system \(\dot x=A(t)x\) in terms of the Lyapunov function \(V=\langle G(t)x,x\rangle\) with almost periodic \(A(t)\) and \(G(t)\). It was shown that for the indicated class the condition on the derivative \(\overset\circ V\) can be essentially weakened in comparison with Lyapunov's theorem for general linear systems. In the present article, we obtain a difference analog of the result.
scientific article; zbMATH DE number 1023988