Stability in linear systems having a time-variable parameter

Abstract

Stability of a linear system having a sinusoidally varying physical parameter is determined by studying the characteristic equation to the system. Conditions for asymptotic stability are derived from theorems of Floquet, Cauchy, and Poincar. These lead to an infinite determinant, approximated by a finite determinant, from which conditions on the physical parameters for stability are determined. Experimental results on two systems show the validity of the approximation, and also indicate that a vibratory element can induce stability in an otherwise unstable system.