• Journal of Electrical Engineering and Technology
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• v.6 no.6
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• pp.874-882
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• 2011

The decoupling design for the one-degree-of-freedom controller system is treated within the $H_{\infty}$ framework. In the present study, we demonstrate that the $H_{\infty}$ performance problem in the decoupling design is reduced into interpolation problems on scalar functions. To guarantee the properness of decoupling controllers and the overall transfer matrix, the relative degree conditions on the interpolating scalar functions are derived. To find the interpolating functions with relative degree constraints, Nevanlinna-Pick algorithm with starting function constraint is utilized in the present study. An illustrative example is given to provide details regarding the solution.