ROBUST SCHUR POLYNOMIAL STABILITY AND KHARITONOV'S THEOREM.

Abstract

Robust stability properties for certain Schur polynomials are considered. By plotting coefficient variations in planes defined by variable pairs and requiring in each such plane that the region of obtained coefficients to be bounded by lines of slope 45 degree , 90 degree and 135 degree , it is shown that stability for all polynomials defined by corner points is necessary and sufficient for stability of all polynomials defined by any points in the region. Using this idea, one can construct several necessity and differing sufficiency conditions for the stability of polynomials where each coefficient can vary independently in a particular interval. As the sufficiency conditions become closer to necessity conditions, the number of distinct polynomials for which stability has to be tested increases. These results improve on V. L. Kharitonov's theorem (1979) regarding robust stabilizability.