Persistency of excitation criteria for linear,multivariable, time-varying systems

For continuous-time, multiple-input, multiple-output, linear systems, we present conditions under which the persistency of excitation of one regression vector implies the persistency of another regression vector derived from the first via a linear, dynamical transformation. We then introduce a definition of sufficient richness for vector input signals in the form of a persistency of excitation condition on a basis regression vector. Finally we establish input conditions which guarantee the persistency of excitation of a large class of regression vectors obtained from both time-invariant and time-varying systems. The work reported was performed while both authors were at the Department of Systems Engineering, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, A.C.T. 2601, Australia.