By Petros A. Ioannou, Petar V. Kokotovic
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Additional info for Adaptive Systems with Reduced Models
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. AC-20, pp. 111-113, February 1975.  J . H . Chow, '~reservatlon of Controllability in Linear Time-lnvarlant Perturbed Systems," Int. J. Control, Sol. 25, No. 5, pp. 697-704, 1975,  K . S . Narendra, "Stable Identification Schemes," System Identification: Advances ~ndCaee Studies, Academic Press, New York, 1976.
697-704, 1975,  K . S . Narendra, "Stable Identification Schemes," System Identification: Advances ~ndCaee Studies, Academic Press, New York, 1976.  P. Kudva and K. S. Narendra, "Synthesis of an Adaptive Observer Using Lyapunov's Direct Method," Int. J. Control, Vol. 18, pp. 1201-1210, December 1973. [i0] K. S. Narendra and P. Kudva, "Stable Adaptive Schemes for System Identification and Control, Part II," IEEE Trans. on Syet~ne, Man, and Cybernetics, Vol. SMC-4, No. 6, pp. 552-560, November 1974.
7). The adaptive observer [ii] for observing the state x and estimating p* when D(t) ffi0 is reviewed below. 116) c z^x. 118) where G = GT> 0 and el A= ~_y. 119) d~ -- -GMT (t) ccTe. 120) Our use of e to denote both exp and the state error is obvious from the context and should cause no confusion. 13) where FT - [-AT 0T], Q T [eT(0),0T], R = H = "-M(t)GMT(tlcc T A n (t) _ ~ Z (t) cC r M(t) + [ly,lu]] . 1211 0 In this case the dominant richness appears indirectly as a sufficient condition for 0 < kll < f 0 t+T MT(T)ccTM(T)dT < k21 for all t>0.