A geometric characterisation of the persistence of excitation condition for sequences generated by discrete-time autonomous systems

Abstract

The persistence of excitation condition for sequences generated by time-invariant, discrete-time, autonomous linear and nonlinear systems is studied. A rank condition is shown to be equivalent to the persistence of excitation of sequences generated by the class of systems considered, consistently with the results established by the authors for the continuous-time case. The condition is geometric in nature and can be checked a priori for a Poisson stable system, that is, without knowing explicitly the state trajectories of the system. The significance of the ideas and tools presented is illustrated by means of simple examples.