A generalization of Kharitonov´s theorem; Robust stability of interval plants

The robust stability problem is considered for interval plants, in the case of single input (multioutput) or single output (multi-input) systems. A necessary and sufficient condition for the robust stabilization of such plants is developed, using a generalization of V. L. Kharitonov´s theorem (1978). The generalization given provides necessary and sufficient conditions for the stability of a family of polynomials delta (s)=Q/sub 1/(s)P/sub 1/(s)+ . . . +Q/sub m/(s)P/sub m/(s), where the Q/sub i/ are fixed and the P/sub i/ are interval polynomials, the coefficients of which are regarded 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. It is shown that for special classes of polynomials Q/sub i/(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.<>