Reduced Sensitivity Solutions to Global Linearisation of the Pole Assignment Map

The problem of pole assignment, by static output feedback controllers has been tackled as far as solvability conditions and the computation of solutions when they exist by a powerful method referred to as global linearisation. This is based on asymptotic linearisation (around a degenerate point) of the pole placement map. The essence of the present approach is to reduce the multilinear nature of the problem to the solution of a linear set of equations. The solution is given in closed form in terms of a one-parameter family of static feedback compensators, for which the closed-loop poles approach the required ones as ǫ → 0. The use of degenerate compensators makes the method numerically sensitive. This paper develops further the global linearisation framework by developing numerical techniques which make the method less sensitive to the use of degenerate solutions as the basis of the methodology. The proposed new computational framework for finding output feedback controllers improves considerably the sensitivity properties by using a predictor-corrector numerical method based on homotopy continuation. The modified method guarantees the maximum distance from the degenerate point. The current numerical method developed for the constant output feedback extends also to the case of dynamic output feedback.