Analysis of Transient Processes in Stable Scalar Linear Discrete-Time Systems

Abstract

We consider stable linear scalar systems described by homogenous difference equations with nonzero initial conditions. We show that, at finite time instants, solutions can deviate far from the equilibrium. For classes of root locations and initial conditions, closed-form estimates are obtained for the magnitude of deviations and the instant of the maximum deviation. Simple conditions on the presence of deviations are formulated and the issues are discussed of how typical are these effects.