Guaranteed Control for Coupled Lossless Transmission Lines Terminated by a Nonlinear Lumped Circuits

Abstract

New stability result is obtained for a multiple interconnected lossless transmission line system which are each terminated by a lumped nonlinear circuit. The result was obtained by first deriving a neutral functional differential system with infinite delays (NFDSID) using the telegrapher's equation to reduce the governing equation of the voltage and current changes from the mutually interconnected lossless transmission line system. A delay-dependent stability results sufficient to make the NFDSID uniformly asymptotically stable is then developed by using the Lyapunov Razumikhin's method through a model transformation technique andLyapunov matrix equation.