This article considers a robust decoupling controller design for a multivariate control system with parameter uncertainties for the hot rolling mill process. The left and right coprime factorization theory is used to properly select the free and weighting matrices. The necessary and sufficient conditions for robust decoupling controller are also proposed. Then, by analyzing the changes in the dynamic response resulting from perturbations in the tension and angle system parameters in the hot

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... p rolling process, a modified multivariate model is developed. Furthermore, the selection method for a practical weighting function is studied, so that the robust and decoupling performance can be simultaneously realized for the controller implementation. Finally, the effectiveness of the proposed control approach is demonstrated using a case study from an industrial hot rolling mill.