On the robustness of low-order Schur polynomials

Robust Schur stability conditions are obtained for polynomials of orders two to five. For n=2 and 3, the conditions obtained are related to stability of the corner points, while for n=4 and 5, the conditions are related to stability of corner and possible supplementary points. The number of points increases substantially as the polynomial order increases. The obtained results are of importance in the robust design of control systems. The difficulty in extending the approach to higher-order polynomials is discussed. Special cases for such extensions are mentioned. Further applications of the results obtained may be of use in the stability study of two-dimensional systems. Some examples for the application of the stability conditions are given and, in particular, the two counterexamples presented in the literature are discussed