Arbitrarily small sensitivity in multiple-input-output uncertain feedback systems

A square, linear time invariant, multiple-input multiple-output plant R is considered, known only to belong to a set {R}. The plant is embedded in a feedback structure designed such that the closed loop response belongs to a specified set for all R ε{lunate} {R}. This paper develops sufficient conditions on the uncertain set {R} such that arbitrarily small sensitivity and internal stability can be achieved by the Horowitz synthesis method. Specifically, we show that, in addition to generalized single-input single-output like conditions, there exists a condition on the pole/zero excess of the controller.