This study is motivated by a need to effectively determine the difference between a system fault and normal system operation under parametric uncertainty using eigenstructure analysis. This involves computational robustness of eigenvectors in linear state space systems dependent upon uncertain parameters. The work involves the development of practical algorithms which provide for computable robustness measures on the achievable set of eigenvectors associated with certain state space matrix constructions. To make connections to a class of systems for which eigenvalue and characteristic root robustness are well understood, the work begins by focusing on companion form matrices associated with a polynomial whose coefficients lie in specified intervals. The work uses an extension of the well known theories of Kharitonov that provides computational efficient tests for containment of the roots of the polynomial (and eigenvalues of the companion matrices) in “desirable” regions, such as the left half of the complex plane.
 T. Alt and F. Jabbari, “Robustness Bounds for Linear Systems under Uncertainty: Eigenvalues Inside a Wedge,” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 4, 1993, pp. 695-701. doi:10.2514/3.21069
 P. Michelberger, P. Varlaki, A. Keresztes and J. Bokor, “Design of Active Suspension System for Road Vehicles: An Eigenstructure Assignment Approach,” Proceedings of the 23rd Fédération Internationale des Sociétés d’Ingénieurs des Techniques de l’Automobile (FISITA) World Automotive Congress, Torino, 1990, pp. 213-218.
 R. Patton and J. Chen, “On Eigenstructure Assignment for Robust Fault Diagnosis,” International Journal of Robust and Nonlinear Control, Vol. 10, No. 14, 2000, pp. 1193-1208. doi:10.1002/1099-1239(20001215)10:14<1193::AID-RNC523>3.0.CO;2-R
 S. Eisenstat and I. Ipsen, “Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds,” SIAM Journal on Matrix Analysis and Applications, Vol. 20, No. 1, 1998, pp. 149-158. doi:10.1137/S0895479897323282
 F. Bazán, “Matrix Polynomials with Partially Prescribed Eigenstructure: Eigenvalue Sensitivity and Condition Estimation,” Computational and Applied Mathematics, Vol. 24, No. 3, 2005, pp. 365-392. doi:10.1590/S0101-82052005000300003