I did search the question database regarding this question, and although one or two questions came close, they didn't really address my specific question.
In adaptive control based on minimizing tracking error (e.g. between plant and model), the designer is free to chose a cost function. More often than not the cost is selected as a function of the squared error.
But I've found in some practical applications that I can achieve a more robust controller by using absolute error. I understand that absolute error provides a more uniform weighting on the size of the error, and I suspect the squared error tends to 'wind-up' the adaptive controller with initially large errors. But I'm not sure how to show this in a generalized way. So I have two questions regarding this:
Is there perhaps a simple analysis that can demonstrate the stability characteristics between absolute and squared error choices in the cost function?
Any references on the matter?