Sufficient LMI conditions for reduced-order multi-objective H2/H∞H2/H∞ control of LTI systems

This paper presents a novel projection lemma based linear matrix inequality (LMI) framework to design reduced-order multi-objective H2/H∞H2/H∞ controllers for linear time-invariant systems. This framework relies on a set of full-order H2/H∞H2/H∞ controllers, which are used as parameters in sufficient LMIs for the reduced-order controller design. Continuous-time and discrete-time controller designs are treated in a unified fashion. It is theoretically and numerically demonstrated that the approach allows the computation of reduced-order controllers that are potentially less conservative than full-order designs resulting from well-known LMI approaches. Various comparisons with existing reduced-order controller design approaches illustrate the potential of the proposed framework of sufficient LMIs.