Global regulation performance indices and the orthogonality of the eigenvector set

The relationship between the global regulation dynamic performance indices and the orthogonality of the system eigenvectors is discussed. The result has previously been presented by the authors (1993) without proof. The relationship is analyzed and the result is proved. It is shown that among all systems with the same distinct pole set, the system with a complete orthonormal eigenvector set has minimum global regulation index values. It also means that the calculable regulation dynamic performance indices are the good measurement of the system performance, since it has been proved that better orthogonality of the system eigenvector set brings lager robust stable bound of the system.