An alternative proof of Kharitonov's theorem Academic Article uri icon


  • We present here an alternative proof of Kharitonovs theorem for real polynomials. The proof shows that if an unstable root exists in the interval family, then another unstable root must also show up in what we call the Kharitonov plane which is delimited by the four Kharitonov polynomials. This fact is proved by using a simple lemma dealing with convex combinations of polynomials. We then make use of a well-known result to prove that when the four Kharitonov polynomials are stable, the Kharitonov plane must also be stable, and this contradiction proves the theorem. 1989 IEEE

published proceedings

  • IEEE Transactions on Automatic Control

author list (cited authors)

  • Chapellat, H., & Bhattacharyya, S. P.

citation count

  • 49

complete list of authors

  • Chapellat, H||Bhattacharyya, SP

publication date

  • April 1989