Robustness of optimally robust controllers

Abstract

The largest robust stability radius gamma (P/sub 0/) of a system P/sub 0/ is defined as the radius of the largest ball B/sub max/ in the gap metric centered at P/sub 0/ which can be stabilized by one single controller. Any controller which stabilizes B/sub max/ is called an optimally robust controller of P/sub 0/. Any controller, regarded as a system, should have its own largest robust stability radius also. In the paper it is shown that the largest robust stability radius of any optimally robust controller of P/sub 0/ is larger than or equal to gamma (P/sub 0/). Moreover, the variation of the closed-loop transfer matrix caused by the perturbation of the system is estimated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>