A generalization of Mikhailov's criterion with applications

Mikhailov's criterion states that the hodograph /spl delta/(j/spl omega/) of a real, n/sup th/ degree, Hurwitz stable polynomial /spl delta/(s) turns strictly counterclockwise and goes through n quadrants as /spl omega/ runs from 0 to +/spl infin/. In this paper we first give an analytical version of this criterion and then extend this analytical condition to the case of not necessarily Hurwitz polynomials. This generalization is shown to "linearize" some control synthesis problems in the sense that the set of stabilizing controllers is obtained as the solution set of a number of linear equations.