Robust stability of linear systems described by higher-order dynamic equations

The stability radius of higher-order differential and difference systems with respect to various classes of complex affine perturbations of the coefficient matrices is studied. Different perturbation norms are considered. The aim is to derive robustness criteria that are expressed directly in terms of the original data. Previous results on robust stability of Hurwitz and Schur polynomials are extended to monic matrix polynomials. For disturbances acting via a uniform input matrix, computable formulas are obtained, whereas for perturbations with multiple input matrices, structured singular values are involved.<>