ABSTRACT
The lemma on stability works if all eigenvalues of the averaged system have non-zero real parts. We assume that matrix A0 (composed of the mean values of the corresponding elements of A(t)) has no eigenvalues with positive real parts, but has eigenvalues with zero real parts. In this case the study of the stability of the trivial solution of a system
dx
dt = εA(t)x
becomes a more complicated task. In this chapter we present the method developed by I.Z. Shtokalo [1946,
1961] for the investigation of the stability of systems with almost periodic coefficients that are close to constants.
