Arbitrary pole placement via low order dynamic output feedback controllers: a solution in closed form

The problem of pole assignment, by (n₁ McMillan degree) low order dynamic output feedback controllers, is studied for minimal systems described by a proper transfer function matrix G(s)∈R ^mxp(s), with McMillan degree n. In this context the problem is reduced to solving a set of linear equations and this without losing any of the degrees of freedom of the controller. It is shown that the method works generically when n₁⩾n₁´, where n₁´ is the smallest multiple of p satisfying n₁ ´(m+p)+mp>n+n₁´. The framework used here allows also computation of families of controllers, which solve the problem, when solutions exist