Temporal and spatial stability in translation invariant linear resistive networks

Simple algebraic methods are proposed to evaluate the temporal and spatial stability of translation invariant linear resistive networks. Temporal stability is discussed for a finite number of nodes n. The proposed method evaluates stability of a Toeplitz pencil A/sub n/(a)+/spl mu/B/sub n/(b) in terms of parameters a/sub i/ and b/sub i/. In many cases a simple method allows one to verify positive definition of B/sub n/(b) in terms of b/sub i/ only.