Robust Output Dynamic Min-Max Control for Discrete Uncertain Systems

Abstract

Min-max control is a robust control, which guarantees stability in the presence of matched uncertainties. The basic min-max control is a static state feedback law. Recently, the applicability conditions of the discrete static min-max control through the output, have been derived. In this paper, the results for the output static min-max control are further extended to a class of output dynamic min-max controllers, and a general parametrization of all such controllers is derived. The dynamic output min-max control is shown to exist in many circumstances in which the output static min-max control does not exist, and usually allows for broader bounds on uncertainties. Another family of robust output min-max controllers - constructed from an asymptotic observer which is insensitive to uncertainties and a state min-max control - is derived, and shown to have the same stability properties as that of the full state feedback min-max control.