Stability and instability criteria for nonlinear distributed networks

Publisher Website
Google Scholar
Abstract
Electrical networks consisting of lumped linear and memoryless nonlinear elements and an arbitrary number of lossless transmission lines are considered. It is shown that a large class of such networks can be described by a system of functional-differential equations having the form\dot{x}(t) =f(x_{t}), where the state of the system at timet \geq 0is represented byx_{t}, a point in the spaceC_{H}((- \infty,0], E^{n})of bounded continuous functions mapping the interval(-\infty , 0]intoE^{n}, with the compact open topology, and the functionfmappingC_{H}(( - \infty, 0], E^{n})intoE^{n}is continuous and Lipschitzian. A Lyapunov functional is presented and used to obtain several theorems concerning the stability and instability of the equilibrium solution of such networks.

This publication has 8 references indexed in Scilit: