BIBO stability and simple tests

Abstract

BIBO stability of constant coefficient linear systems, whether described by differential or difference equations, is determined by the pole locations of the closed loop systems. These poles are, by definition, the roots of the denominator polynomial in transfer function representations and of the characteristic equation of the A matrix in state-space representations. These poles must lie in the left-half plane for continuous time systems and within the unit circle for discrete time systems. The straightforward way of checking this is to compute the poles. An alternative that is easy and can lead to other insights is to process the coefficients of the denominator polynomial of the transfer function, which is the same as the determinant of the state space dynamics matrix. This chapter demonstrates those tests and shows how they may be used three different ways.