GLOBAL ASYMPTOTIC LINEARIZATION OF THE POLE-PLACEMENT MAP - A CLOSED-FORM SOLUTION FOR THE CONSTANT OUTPUT-FEEDBACK PROBLEM

The problem of pole assignment, by constant output feedback controller s, is studied for minimal systems described by a proper transfer funct ion matrix G(s) is an element of R(mxp)(s) With McMillan degree n. A n ew method is presented based on asymptotic linearisation (around a deg enerate point) of the pole placement map related to the problem. The e ssence of the present approach is to reduce the multilinear nature of the problem to one of solving a linear set of equations, and this is a chieved without losing any of the degrees of freedom in the controller . The solution is given in closed form in terms of a one-parameter (ep silon) family of Static feedback compensators, for which the closed-lo op poles approach the required ones as epsilon --> 0. Conditions for t he generic, as well as exact, solvability of the arbitrary pole placem ent problem are given in terms of the numbers m, p, n and the rank of a new system invariant, the D-restricted Plucker matrix. It is shown t hat the method works generically when mp > n, which (along with the bo undary case mp = n) is the best possible condition as far as the numbe r of states of the open-loop system is concerned, for achieving arbitr ary pole placement via constant output feedback.