An extreme value problem in a linear sampled-data feedback system

When an uncorrelated, wide-band Markov noise process contaminates the input signal to a linear sampled-data feedback system, the extreme values of the mean-square true error and the mean-square apparent error are shown to occur for most practical purposes at the same value of the scalar loop gain. The gain parameter in an adaptive system may therefore be adjusted for minimum mean-square true error by minimizing the corresponding apparent error. An actual practical example is used to illustrate the result.