Stability Analysis of Neutral Functional Differential Equations Arising in Partial Element Equivalent Circuit Models

Abstract

Neutral Functional Differential Equations (NFDEs) arise in the study of the Partial Element Equivalent Circuit (PEEC) model with time delays. We present sufficient conditions for asymptotic stability and global stability in the delays of the PEEC NFDE’s, using Lyapunov-Razumikhin function methods.. We develop, for the first time, a standard mixing-type nonlinearity for the PEEC NFDEs. Introducing time invariant and time varying nonlinear perturbation to the PEEC NFDEs, we develop sufficient conditions for stability of the nonlinear perturbed PEEC NFDEs and convergence of the nonlinear system to the original stable linear autonomous system. We also develop sufficient conditions for stability and convergence of the nonlinear perturbed PEEC NFDEs.