Methods for linear systems of circuit delay differential equations of neutral type

TLDR

Delay differential equations arise in circuit theory, where delayed elements—especially in transmission lines and partial element equivalent circuits—are increasingly important for high‑performance VLSI systems. The study investigates contractivity conditions and sufficient criteria for asymptotic stability of the zero solution in DDE systems via a suitable reformulation. We solve these systems with solvers analogous to conventional ODE circuit simulators, applying a reformulation of the system to analyze stability.

Abstract

Delay differential equations (DDEs) occur in many different fields including circuit theory. Circuits which include delayed elements have become more important due to the increase in performance of VLSI systems. The two types of circuits which include elements with delay are transmission lines and partial element equivalent circuits. The solution of systems which include these circuit elements are performed with solvers similar to conventional ODE circuits simulators. Since DDE solvers are more fragile with respect to stability, we investigate the conditions for contractivity and determine sufficient conditions for the asymptotic stability of the zero solution by utilizing a suitable reformulation of the system.