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We obtain an optimal 2 H decoupling controller for rectangular plants in a standard twodegree-of-freedom controller configuration model. The class of all stabilizing and decoupling loop controllers is parameterized in terms of free diagonal parameter matrices. We determined the optimal decoupling controller from these free parameters. Inner-outer factorization and the Khatri-Rao product expression for the vector operation to a diagonal matrix are the key steps in obtaining the 2 H optimal solution. We provide a compact set of assumptions to assure the existence of the optimal solution.

-Necessary and sufficient conditions for the existence of diagonal, block-diagonal, and triangular decoupling controllers in linear multivariable systems for the most general setting are presented. The plant model in this study is sufficiently general to accommodate non-square plant and non-unity feedback cases with one-degree-of-freedom (1DOF) or two-degree-of-freedom (2DOF) controller configuration. The existence condition is described in terms of rank conditions on the coefficient matrices in partial fraction expansions.

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