In this paper, analytic expressions are derived for the complex and real stability radii of non-monic polynomial matrices with respect to an arbitrary stability region of the complex plane. Numerical issues for computing these radii for different perturbation structures are also considered with application to robust stability of Hurwitz and Schur polynomial matrices.

Explicit schemes are attractive for obtaining finite difference solutions to partial differential equations because of their simplicity. However this feature is undermined by the severe restriction on stability that the schemes suffer. One method that appears to have better stability properties is Charlie’s method. The stability region of this method applied to a one-dimensional heat conduction...