Robust assignment of polynomial matrix polytopes

Assignment of the coefficients of factors of the characteristic polynomial of an uncertain multi-input multi-output system to polytopic regions is considered. Owing to a special upper triangular form of the desired closed-loop polynomial matrix, this formulation leads to an affine design problem. This design is closer to the ultimate pole placement than the assignment of the characteristic polynomial direct. As a result, one obtains a set of affine inequalities with respect to the controller coefficients. The solution (if it exists) of these inequalities then defines all admissible controllers.