By Petros A. Ioannou, Petar V. Kokotovic
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Extra info for Adaptive Systems with Reduced Models
125) does not exclude the possibility that the may be significant. In fact if u contains frequencies of the fast state q will be of 0(1), Hn will be persistent for all ~ and there- fore robustness will be lost. Our results also show that the presence of parasltics may cause loss of richness, if the richness is achieved with frequencies in the parasitic range. On the other hand, the dominantly rich inputs guarantee the robustness property. G : -4n + . o . 13o) y = [l,0)x. 49) with A21 = 0 and hence L = O, A22 = Af, ~ i = A.
5-24, January 1977.  B . D . O . Anderson, "Exponential Stability of Linear Equations Arising in Adaptive Identification," IEEE Trans. on Automatic Control, Vol. AC-22, pp. 83-88, February 1977.  J . C . Yuan and W. M. Wonham, "Probing Signals for Model Reference Identification," IEEE T ~ s . on Automatic Control, pp. 530-538, August 1977.  P . V . Kokotovlc and A. H. Haddad, "Controllability and Time-Optlmal Control of Systems with Slow and Fast Modes," IEEE Trans. on Automatic Control, Vol.
L O~ i . . I O! i , , , I , , , ' o~ b"£ 36 The improvement of the bound by making the convergence rate m 2 larger may require trial and error selection of the adaptive gains. 135) (1 + n k 2 max ~[G]) 2 gives more information about the dependence of the error bound on other quantities. In this case m 2 is the largest when max %[G] - mln %[G]. 135) that the error bound will be higher when the order n of the dominant part of the plant is higher. 2,8, REFERENCES  P. V. Kokotovic, R. E. , and P.