In Example 5.18 (noise cancellation), there are two sign errors in equation (5.26) that are propagated through the next several lines. The corrected text should read (with changes in red):
Assuming for simplicity that , introduce , , and . Then
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(5.26)
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We will achieve noise cancellation if we can find a feedback law for changing the parameters and so that the error goes to zero. To do this we choose
as a candidate Lyapunov function for
equation (5.26). The derivative of is
Choosing
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(5.27)
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we find that , and it follows that the
quadratic function will decrease as long as .