Pole placement design: an interpolation theoretic approach

Abstract

We present a new frequency domain parametrization for the family of controllers which place the poles of the closed loop transfer function in a given region in the complex plane. We use the Q-parametrization to obtain an affine representation for the closed loop transfer functions. It is then possible to recast the pole placement problem into a constrained tangential interpolation problem in terms of Q. Making some full rankness assumptions, we reduce the resulting two-sided interpolation problem into a solvable left-sided problem and solve the final form by the so called generalized Schur algorithm. The proposed technique is numerically efficient and stable and provides new theoretical insight into the problem.