A generalization of Kharitonov's theorem; Robust stability of interval plants Academic Article uri icon


  • This paper is motivated by the problem of the robust stability of a linear time-invariant control system containing a plant, some (or all) of whose transfer function coefficients are subject to perturbation within prescribed ranges. The family of transfer functions corresponding to this box in parameter space is referred to as an interval plant. The main contribution of the paper is a generalization of Kharitonov's theorem [1] for determining the robust stability of such systems. The generalization given here provides necessary and sufficient conditions for the stability of a family of polynomials (s) = Q1(s)P1(s) + + Qm(s)Pm(s),where the Q1's are fixed and the P1's are interval polynomials, the coefficients of which we regard as a point in parameter space which varies within a prescribed box. This generalization called the box theorem reduces the question of the stability of the box in parameter space to the equivalent problem of the stability of a prescribed set of line segments. The number of these line segments, m X 4mis independent of the dimension of the parameter space. Moreover, it is shown, that for special classes of polynomials Q1(s) the set of line segments collapses to a set of points, and this version of the box theorem in turn reduces to Kharitonov's original theorem. 1989 IEEE

published proceedings

  • IEEE Transactions on Automatic Control

author list (cited authors)

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

citation count

  • 231

complete list of authors

  • Chapellat, H||Bhattacharyya, SP

publication date

  • March 1989