Eigenvalue perturbation models for robust control

This paper presents a nonconservative description of the regions containing the eigenvalues of a diagonal matrix, perturbed by the set of all unknown, Euclidean norm bounded matrices. This is extended to real valued block diagonal matrices where each two-by-two block reveals a complex conjugate pair of eigenvalues. A weighting matrix allows one to specify the exact size of the perturbation to each of the eigenvalues. An identical result is obtained for real valued perturbations. This result is motivated by, and applied to, the modeling of frequency and damping perturbations in models of flexible structures. The resulting perturbation description fits within the established H_∞ robust control framework and, in certain situations, is less conservative than the more standard additive or multiplicative perturbation models