Robust controllers for uncertain linear multivariable systems

This paper is addressed to three distinct yet related topics in the design of controllers for imprecisely known linear multivariable systems. In the first part, it is supposed that the plant to be stabilized is subject to additive or multiplicative uncertainties, and necessary and sufficient conditions are derived for the existence of a controller that stabilizes all plants within this band of uncertainty. In the second part, in contrast with the first part, it is supposed that the number of unstable poles of the plant to be stabilized is not precisely known. The type of plant uncertainty is the so-called “stable-factor” uncertainty, and necessary and sufficient conditions are given for robust stabilization. In the third part, the model of uncertainty is a ball in the space of rational matrices metrized by the so-called graph metric, and sufficient conditions for robust stabilization are derived.