New dilated LMI conditions for the single channeled multiobjective static state feedback controller synthesis in cotinuous-time systemes

This paper introduces new dilated sufficient LMI conditions for the single channeled multiobjective static state feedback controller synthesis in linear continuous-time systems for which, optimality is defined in terms of H₂ and H_∞ performance criteria jointly applied to a single channel. These conditions provide sub-optimal synthesis procedures that have the advantage of keeping the controller parameters independent of the Lyapunov matrix and offering supplementary degrees of freedom. The proposed dilated LMI conditions always encompass the standard ones. It follows that much less conservatism is possible in comparison to the currently used standard LMI based multiobjective state feedback synthesis procedures. A numerical simulation is presented and the advantage of the proposed synthesis methods.