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IMA Journal of Mathematical Control and Information 1990 7(3):235-248; doi:10.1093/imamci/7.3.235
© 1990 by Institute of Mathematics and its Applications
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A Simple Geometrical Proof of the Box Theorem

C. B. SOH

School of Electrical and Electronic Engineering, Nanyang Technological Institute Nanyang Avenue, Singapore 2263

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) = Q1(s)P1(s) +...+ Qm(s)Pm(s), where Q1(s) are fixed real polynomials and P1(s) are real interval polynomials, is Hurwitz if and only if a prescribed set of m x 4m 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


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