Abstract: A persistency of excitation result for nonminimal models of systems having purely deterministic disturbances has been given recently in [1]. In this note we give a direct and simple proof for the case of bounded signals of the result of [1] and show, via a counterexample, that an assumption on system signals boundedness which does not appear in [1] is necessary when arbitrary unbounded signals are allowable. Finally, we give a proper persistency of excitation result which does not require signal boundedness for the case when the system input consists of a bounded external signal and of a constant coefficient feedback component.
B I B L I O G R A F I A1. G. C. Goodwin , J. P. Norton and Î. N. Viswanathan "Persistency of excitation for nonminimal models of systems having purely deterministic disturbances", IEEE Trans. Automat. Contr., vol. AC-25, pp.449 -456 1985
2. B. D. O. Anderson and C. R. Johnstone Jr. "Exponential convergence of adaptive identification and control algorithms", Automatica, vol. 18, pp.1 -13 1982
H. Elliott , R. Cristi and M. Das "Global stability of adaptive pole placement algorithms", IEEE Trans. Automat. Contr., vol. AC-30, pp.348 -356 1985
3. G. C. Goodwin and E. K. Teoh "Persistency of excitation in the presence of possible unbounded signals", IEEE Trans. Automat. Contr., vol. AC-30, pp.595 -599 1985
4. D. Janecki "Globally stable and exponentially convergent adaptive control", Int. J. Contr., vol. 43, pp.601 -613 1986 
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