On ultimate boundedness control of uncertain systems in the absence of matching assumptions

This paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required. Instead of imposing the so-called matching conditions of previous authors, a certain "decomposition" of the dynamics is performed. The resulting "decomposed system" has two parts-a matched portion and a mismatched portion. A certain measure of mismatch <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> is defined and it is shown that effective control is possible as long as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> does not exceed some critical mismatch threshold M * . It is seen that this threshold depends on the choice of feedback. Hence, it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions.