Sensitivity analysis of the roots of the characteristic polynomial and stability of non-conservative systems

Abstract

The effect of small dissipative and gyroscopic forces on the stability of a linear autonomous non-conservative system of general type is studied. The problem is investigated by sensitivity analysis of multiple roots of the characteristic polynomial of the system whose coefficients are expressed through the invariants of the matrices involved. For systems with two degrees of freedom an explicit approximation of the domain of asymptotic stability is found. As a mechanical example the problem of stability of a mass sliding over a conveyor belt is considered in detail. I. INTRODUCTION