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           

Therefore the q11 template is 14 dB in height and the 11cτ bound can be ignored resulting in the optimal bound for the 1,1 loop being essentially the same as the tracking bound due to τ11. Note that

0|| 004.0

11 >≈

c for

τ

For the frequency range of 0.1 to 2 rad/sec the bounds on L1oare obtained on the basis of11τ . Forvalues of frequency greater than 2 rad/sec the bounds are obtained based on the following:

b

b

b

b ≥+≥+

(b) For the bounds on L2o use

b ≤

+

for the “low frequency range.” For e.g., b21/b11 = 0.01/0.65 → −36 dB at ω = 2. This gives the bound on L2o(j2) at approximately +10 dB at – 100o which is much tougher than that on L1o(j2). Thus, a “trade-off” is in order to improve (lower) the bounds on L2o at the expense of raising the bounds on L1o. It is left to the reader to determine the bounds with b11 = 0.18 and compare them with those determined for the original value of b11.