A new method for singular value loop shaping in design of multiple-channel controllers

In this note, simple symmetric interval bounds on the singular values of a matrix based on its Gershgorin disks are proposed. This allows the Gershgorin theorem to be used not only to provide information about the location of the eigenvalues of a matrix but also its singular values. This is utilized for the proposition of a new design technique for singular value loop shaping based on the diagonal dominance methodology for design of linear multivariable plants. In return, this allows multiple-channel simply structured controllers to be designed with a view to robustness and to meet constraints and specifications on the behavior of its singular values. A design example is given demonstrating the effectiveness of this approach.