Delay-Independent Stability of Nonlinear Delay Differential Equations via Isospectral Reduction

Abstract

Time delays arise naturally in a wide range of natural and technological systems, yet their influence on the stability remains a challenge to characterize, particularly for nonlinear systems. In this paper, we develop a stability framework that yields a delay-independent criterion for global exponential stability in a broad class of nonlinear, nonautonomous delay differential equations. Our approach is based on a novel method that associates the delayed system with a sequence of finite-dimensional matrices of increasing size, which are analyzed using the graph-theoretic technique of isospectral reduction. In contrast to most existing results for nonlinear delay differential equations, which rely on Lyapunov-based methods, our framework provides a general and computationally efficient alternative. As an application, we apply this criterion to analyze consistency in delayed reservoir computing systems, illustrating how the proposed approach can be used to assess stability properties relevant to prediction tasks.