Accession Number : AD0658838

Title :   STABILITY OF LINEAR TIME-VARYING NETWORKS,

Corporate Author : ROME AIR DEVELOPMENT CENTER GRIFFISS AFB N Y

Personal Author(s) : Waag,Robert C. ; Kleckner,Keith R.

Report Date : AUG 1967

Pagination or Media Count : 21

Abstract : Using the second method of Liapunov, both long-known and recent stability results are motivated and presented in a logical treatment. First, the necessary and sufficient conditions for stability of the equilibrium for the A-matrix form of the network equations are summarized. Then, sufficient conditions for network stability are found. This is done in two parts. One outlines conditions that follow directly from the parameter matrices of the various network equation formulations. The other indicates conditions obtained via linear transformations. Stability conditions for fixed networks and two-element-kind time-varying networks follow as special cases of this general treatment. The results are interpreted in terms of phase space concepts and restrictions on element pumps. Examples of each of the stability conditions are given and comparisons are made between different techniques for determining network stability. In particular, a case is discussed in which the stability of a network is predicted by the present linear transformation technique but is not predicted by the modified energy function method recently given by Kuhn. (Author)

Descriptors :   (*NETWORKS, THEORY), ELECTRICAL NETWORKS, STABILITY, TIME, LINEAR SYSTEMS, MATRICES(MATHEMATICS), TRANSFORMATIONS(MATHEMATICS)

Subject Categories : Electrical and Electronic Equipment

Distribution Statement : APPROVED FOR PUBLIC RELEASE