An Optimal H₂Decoupling Design for Non-Square Plant Systems based on the Two-Degree-of-Freedom Standard Model

An Optimal H₂Decoupling Design for Non-Square Plant Systems based on the Two-Degree-of-Freedom Standard Model

We obtain an optimal decoupling controller for rectangular plants in a standard two-degree-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 optimal solution. We provide a compact set of assumptions to assure the existence of the optimal solution.

We obtain an optimal decoupling controller for rectangular plants in a standard two-degree-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 optimal solution. We provide a compact set of assumptions to assure the existence of the optimal solution.