Modeling Nonlinear Energy Transmission Chains Via Volterra Series: Convergence Criteria and Stability Bounds Under Periodic Excitation

This paper derives sufficient conditions for the convergence of Volterra series representing solutions to a class of nonlinear integral equations that model energy objects’ dynamic networks with periodic input signals. By formulating the system’s response through a nonlinear integral equation, we establish rigorous criteria for the absolute convergence of the Volterra series expansion. Specifically, we analyze energy objects’ networks containing ideal bandpass filters excited by trigonometric polynomial inputs, a configuration common in simplified analyses of physically realizable systems. For energy systems’ resistive nonlinear chains, we demonstrate that the Volterra series reduces to a power series and provide explicit estimates of its convergence radius (Theoretical statement 3). Additionally, Theoretical statements 1 and 2 present generalized convergence criteria based on the minimization of a functional over a constrained spatial domain, extending prior results for NARX-type systems. The results can contribute to bridging theoretical analysis with engineering applications, offering practical tools for designing nonlinear energy systems’ chains with predictable dynamics, such as those found in power electronics and signal processing systems.