By King A.S.
Read or Download [Article] A Study of the Effect of a Magnetic Field on Electric Furnace Spectra PDF
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Extra info for [Article] A Study of the Effect of a Magnetic Field on Electric Furnace Spectra
7607] O. 8181. 3) gives the optimal quadratic guaranteed 34 2. 2 shows a plot of the mean square error as a function of the uncertain parameter 6.. From this plot. it can be seen that for all admissible values of the uncertain parameter, the corresponding mean square error is less than the calculated quadratic guaranteed cost bound. Note that in this plot, only constant values of the uncertain parameter were considered. However, the quadratic guaranteed cost bound also holds for time-varying uncertain parameters.
2). 2) has a solution Q > O. Then for any E EO (0. 2) w211 have a stab21Izmg solutIOn Q+ > O. Proof > 0 and Riccati Let IT ~ tQ-l > O. 2) has a solution Q > 0 with E = f'. follows that IT satisfies the Riccati equation IT (A - B1D~ v-Ie) + (A - B1D~ V-Ie)' IT + K' K- e'v- 1e +ITBI A (I - D~ V-I Dl) B~IT + f'ITWIT = 0 ~ where V = f'V + DID~. 15) _ = f'S > O. 18) , Ll. where V = EV + DID~. 17). 17). It follows by a straightforward algebraic manipulation that H - if = [ BC1D' 'I ] (V-I - V-I) [C DIB~] + [00 (E-E 0) W ] .
This completes the proof of the theorem. 3) has the followmg property: Gwen any 6 > 0, there eX2sts a matr2x Q > 0 such that Q+ < Q < Q+ + 6I and the state est2mator zs a quadratzc guaranteed cost state estImator wzth cost matnx Q. 3 Implzes that the steady state error covanance matnx at tIme t sat2sfies the bound for all adm2ssible uncertaint2es for all adm2ssible uncertamt2es ~(t). Th2s bound holds for all8 > O. Hence, ~(t). 2). 2) has a solution Q > O. Then for any E EO (0. 2) w211 have a stab21Izmg solutIOn Q+ > O.