Pole placement by parametric output feedback

This note presents a new analytical solution to the problem of pole placement via constant output feedback under the condition m+p≥nm+p≥n, where nn, mm, and pp are the number of states, inputs and outputs, respectively. The approach is based upon parametric eigenstructure assignment of linear time-invariant multivariable systems in combination with a special explicit formulation of the pole assignment equations. Thus, the resulting analytical solution explicitly offers all remaining mp−nmp−n degrees of freedom beyond eigenvalue assignment which can be used for additional design goals such as response shaping, minimizing the norm of the feedback matrix, and robust control, respectively.