Insensitivity of asymptotically stable matrices to variations in submatrices
Barbara A Shane, Stephen Mark Barnett · International Journal of Systems Science · 1975
For a given asymptotically stable matrix A which has all characteristic roots with negative real parts, changes are found in arbitrary submatrices of A which do not affect the distribution of roots with respect to the imaginary axis. The results give only sufficient, conditions but are relatively straightforward to apply. Application to matrices in companion form enables one or all of the coefficients of a polynomial to be altered without affecting its asymptotic stability. Illustrative numerical examples are given.