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We use frequency domain methods to study robust output regulation of a stable plant in a situation where the controller is only required to be robust with respect to a predefined class of perturbations. We present a characterization for the solvability of the control problem and design a minimal order controller that achieves robustness with respect to a given class of uncertainties. The construction of the controller is illustrated with an example.

Robust regulation of signals generated by infinite-dimensional exosystems have received some attention lately. Robustness have been understood in the sense that strong stability and solvability of a Sylvester equation should imply asymptotic tracking. It is not known what perturbations preserve strong stability or solvability of the Sylvester equation, so it is not entirely clear how robust a robustly regulating controller actually is. The purpose of this article is to give a detailed analysis of the robustness properties of a controller. We give a simple necessary and sufficient condition that guarantees the solvability of the Sylvester equation for single input single output plants. The solvability condition relates smoothness of the reference signals to the solvability of the Sylvester equation and helps us to understand robustness of controllers.

In this paper robust output regulation of distributed parameter systems with infinite-dimensional exosystems is discussed. We divide the problem into two parts, namely robust stabilization and robust regulation, and focus on the latter. Our aim is to give a unified treatment of the problem in time and frequency domains by using blocking zeros.