Robust control design with real-parameter uncertainty and unmodeled dynamics

This paper presents a design methodology for the synthesis of a robust controller that accounts for both unmodeled dynamics and structured real-parameter uncertainty for multiple-input/multiple-output systems. The unmodeled dynamics are assumed to be characterized as a single block dynamic uncertainty at a point in the closed-loop system. In a design aimed at constraining both the H^ norm of a certain disturbance transfer matrix and a quadratic Gaussian performance index under their respective bounds, a surrogate system may be formed by modeling the structured real-parameter uncertainty as additional noise inputs and additional weights at the existing noise inputs and measurement outputs of the system. Application of a Riccati equation approach to this surrogate system then yields a robust controller that, when used in the actual system, will result in a closed-loop system that has the same H^ bound and quadratic Gaussian performance index bound as the surrogate system, even in the presence of given real-parameter variations.