On the Stability of Linear Discrete Dynamic Systems

Abstract

A technique is presented for studying the stability of equilibria of linear discrete dynamic systems involving general types of forces: elastic, nonconservative, dissipative, and gyroscopic. The techniqe is a generalization of the energy method, based upon a restricted version of the general method of Liapunov, and often allows stability to be determined in terms of unspecified parameters. For systems of n degrees of freedom, stability theorems are given which require the existence of an n × n symmetric matrix G having certain properties. Several examples are given to illustrate the method of construction of this matrix and the type of information which it may be expected to yield. In general the method and its results are quite similar to the energy method, but apply even when the energy function does not exist.