This paper is concerned with stable dynamical controller design and system robustness improvement by polynomial pole assignment. Based on a generic controller form for polynomial pole assignment, a formulation of stable dynamical controllers is proposed. The robustness function in the frequency domain used in the H-infinity robust control design is minimised using the freedom provided by polynomial pole assignment. It also shows how to combine time-domain performance specifications provided by pole assignment and robust performance specifications in the frequency domain considered by H-infinity control to realise joint optimum robustness.