Robust Design of Multivariable Feedback Systems with Real Parameter Uncertainty and Unmodelled Dynamics

This paper presents a design methodology for the synthesis of a robust controller that accounts for both unmodelled dynamics and structured real parameter uncertainty for multiple-input, multiple-output systems. 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 modelling 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 which, when used in the actual system, will result in a closed-loop system having the same H¿ bound and quadratic gaussian performance index bound as the surrogate system, even in the presence of given real parameter variations.