A further result on the problem of pole assignment by output feedback

In this paper a new result in the problem of pole assignment by gain output feedback is given. Roughly speaking, this result says that arbitrary pole assignment is possible for almost all systems if
n < r + m + \nu - 1, r > \mu, m \geq \nu
. Here
n, r
and
m
are the number of states, of inputs and of outputs, respectively, and ν and μ are the so-called controllability index and the observability index of the system, respectively. This result extends the author's previous one in [1]. The basic idea in [1] is developed further and its geometrical meaning is amplified. The proof of the theorem itself gives a method of constructing a desired gain matrix. An example is given to show the feasibility of the algorithm.