Abstract
This paper presents a study of the stability of electrical networks consisting of the interconnection of linear lumped parameter elements and memoryless nonlinear elements with uniformly distributed RC lines. It is shown that a large class of such networks can be represented by a functional-differential equation of the retarded type of the form: x ̇ (t) = f(x t), t ⩾ 0 where x t , is the state of the system and f is a nonlinear functional defined on a subset of C((−∞, 0], E n ), the space of all bounded continuous functions mapping the interval (−∞, 0] into E n with the compact open topology. The principal result of this work is the presentation of a functional defined on the function space C, and the use of this functional to derive a set of theorems and corollaries concerning the stability and instability of the network. To illustrate the results, some examples are given.
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