Gain margin based conditions for easy simultaneous achievement of open and closed loop diagonal dominance under unstructured uncertainties

Abstract

This paper proposes a simple and low numerical complexity technique for the simultaneous achievement of open and closed loop diagonal dominance. The method is based on the introduction of a static high gain inner feedback which modifies the plant to attain a diagonal dominant open loop compensated plant over an entire bandwidth of frequencies. The technique can be also applied to uncertain plants. The sufficient conditions derived for the open loop diagonal dominance also assure the simultaneous achievement of closed loop diagonal dominance under weak assumptions on the diagonal elements of the decoupled controller robustly stabilizing the plant. These assumptions agree with the usual closed-loop performance specifications, so that closed-loop diagonal dominance is achieved without any extra complication on the controller design procedure. The main merits of the present method are: applicability to uncertain plants, ease of implementation and low computational cost. Two examples taken from the relevant literature, are given to show the effectiveness of the proposed approach.