A Simple Geometrical Proof of the Box Theorem
Cheong Boon Soh · IMA Journal of Mathematical Control and Information · 1990
Chapellat and Bhattacfaaryya (1989) derived a generalization of Kharitonov‘s theorem for real interval polynomials called the box theorem. The box theorem states that a family of polynomials F(s) = Q 1 (s)P 1 (s) +…+ Q m (s)P m (s), where Q 1 ( s ) are fixed real polynomials and P 1 ( s ) are real interval polynomials, is Hurwitz if and only if a prescribed set of m × 4 m line segments is Hurwitz. Moreover, for special classes of real polynomials Q1 ( s ) (odd or even polynomials), this set collapses to a discrete set of polynomials. In this paper, a simple geometrical proof of the box theorem is presented, and the theorem is also generalized so as to be applicable to complex polynomi