A geometric characterisation of the persistence of excitation condition for sequences generated by discrete-time autonomous systems - Padoan,A; Scarciotti,G; Astolfi,A (IEEE, 2016)
The persistence of excitation condition for sequencesgenerated by time-invariant, discrete-time, autonomouslinear and nonlinear systems is studied. A rank conditionis shown to be equivalent to the persistence of excitationof sequences generated by the class of systems considered,consistently with the results established by the authors for thecontinuous-time case. The condition is geometric in nature andcan 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 illustratedby means of simple examples.