Hyers-Ulam stability for finite-dimensional nonautonomous dynamics

Abstract: The main purpose of this paper is to obtain necessary and sufficient conditions under which a nonautonomous, finite-dimensional and two-sided dynamics generated by a sequence of matrices or a linear ODE exhibits Hyers-Ulam stability. Specifically, in the case of discrete time we consider a nonautonomous difference equation with possibly noninvertible coefficients, while in the case of continuous time we deal with a nonautonomous ordinary differential equation without any bounded growth assumptions.