Dynamic Robust Output 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 discrete static min---max control through the output have been derived. In this paper, the results for 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 under 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. The latter is shown to be a particular case of the dynamic min---max control when the nominal system has no zeros at the origin. In the case where the insensitive observer exists, it is shown that the observer-controller has the same stability properties as those of the full state feedback min---max control.