On a criterion of instability for positive feedback control systems

Abstract

Perturbation of the input in open systems triggers a response which displaces the stationary state. It is shown that the gradients of this stationary displacement are comprised in the inverse matrix of the system. Hence the “trace criterion” of instability is examined in the inverse matrices of some positive and negative feedback oscillatory models. For positive feedback systems the results provide a phenomenological interpretation of instability, in terms of the control properties of the system. An objection to Clarke's conjecture is made.