A generalization of Mikhailov´s criterion with applications

Mikhailov´s criterion states that the hodograph δ(jω) of a real, n^th degree, Hurwitz stable polynomial δ(s) turns strictly counterclockwise and goes through n quadrants as ω runs from 0 to +∞. 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