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.