By Petros A. Ioannou, Petar V. Kokotovic
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Additional resources for Adaptive Systems with Reduced Models
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.  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.
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.
1) are close to the eigenvalues of All. 1). -I We assume that A I exists and It is obvious then that for ~ sufficiently small the n eigenThey are the n "slow" elgen- The remaining m eigenvalues are of 0(~) magnitude. 1) has this two-time scale property. The following lemm, from  extended in [1,2] gives such a bound. 4) A21 + PAll- ~A22 P - ~PAI2P = 0 -i having the property that P÷-A21AII as ~ ÷ 0 . 4) follows from the implicit function theorem. 5) y(k) ffi ClX(k) + ~C2z(k) so that the parasitics are weakly observable from the plant output.
Adaptive Systems with Reduced Models by Petros A. Ioannou, Petar V. Kokotovic
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