Abstract
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.
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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.
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Mareels, I.M.Y., Gevers, M. Persistency of excitation criteria for linear, multivariable, time-varying systems. Math. Control Signal Systems 1, 203–226 (1988). https://doi.org/10.1007/BF02551284
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DOI: https://doi.org/10.1007/BF02551284