By Petros A. Ioannou, Petar V. Kokotovic

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105) =gf m2 fl where gf -- IIA;lll IIAflBf II I[hll IIRII T~2 . 2,6, PARAMETERIZED ADAPTIVE OBSERVER The parameterlzed adaptive observer [ii],[12] is based on a state repre- sentatlon of the plant in which the unknown parameters are contained in an algebraic equation and an error criterion is defined. The adaptive laws are derived by minimizing the error criterion using a gradient technique. 107) n and g satisfies gc T ffiA-F. 106) x ffi e Ft x0 + fteF(t-T)[ gy(x) +Bu(x)]dx 0 + IteF(tmT)Hrl (T) dT.

The same change in the initial error has no effect on the. 5. 6. 44 times and the oscillations of the output error become higher. This shows that when the parasitlcs are sufficiently fast the identification results can be satisfactory. 7. 4% and the output error deviations from zero increase considerably. , in the absence of parasltics, convergence rate is a complicated function of input {u(k)} composition and the step-size matrix F(k). 22) also impact the convergence rate. Clearly, further refine- ment of reduced-order usage composite error bounds will require more detailed descriptions of the convergence rate mechanics.

Morgan and K. S. Narendra, "On the Uniform Asymptotic Stability of Certain Linear Nonautonomous Differential Equations," SIAM J. Control and Opt~ization, Vol. 15, No. i, pp. 5-24, January 1977. [4] 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. [5] J . C . Yuan and W. M. Wonham, "Probing Signals for Model Reference Identification," IEEE T ~ s . on Automatic Control, pp.

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