Necessary conditions for Schur-stability of interval polynomials

New bounds on the coefficient diameter of real Schur-stable interval polynomials are given using techniques from complex analysis. They can be used to unmask interval polynomials at low computational cost as being non-Schur-stable.

[1]  C. Carathéodory Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen , 1907 .

[2]  Huang Lin,et al.  Root locations of an entire polytope of polynomials: It suffices to check the edges , 1987, 1987 American Control Conference.

[3]  Diederich Hinrichsen,et al.  Robustness measures for linear systems with application to stability radii of Hurwitz and Schur polynomials , 1992 .

[4]  R. E. Kalman,et al.  On the Hermite-Fujiwara theorem in stability theory , 1965 .

[5]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[6]  Q. I. Rahman,et al.  Analytic theory of polynomials , 2002 .

[7]  On Coefficient Diameters of Real Schur-Stable Interval Polynomials , 2003 .

[8]  J. Cieslik,et al.  On possibilities of the extension of Kharitonov's stability test for interval polynomials to the discrete-time case , 1987 .

[9]  Prashant Batra,et al.  Bound for all coefficient diameters of real Schur-stable interval polynomials , 2004, IEEE Transactions on Automatic Control.

[10]  Prashant Batra,et al.  On necessary conditions for real robust Schur-stability , 2003, IEEE Trans. Autom. Control..

[11]  Brian D. O. Anderson,et al.  A note on the reduced Schur-Cohn criterion , 1981 .

[12]  B. Ross Barmish,et al.  New Tools for Robustness of Linear Systems , 1993 .

[13]  Thomas Kailath,et al.  On another approach to the Schur-Cohn criterion , 1977 .

[14]  V. Blondel On interval polynomials with no zeros in the unit disc , 1995, IEEE Trans. Autom. Control..

[15]  Shankar P. Bhattacharyya,et al.  Robust Control: The Parametric Approach , 1995 .