Robust multiple objective control by using LMI optimization

The present paper considers the problem of designing guaranteed cost controllers minimizing multiple quadratic performance objectives, for linear systems with parametric uncertainties. The design procedure uses the LMI optimization technique. By setting the multi-objective control problem in an LMI form, one may find the suitable uncertainty decomposition which allows to compute a positive definite solution satisfying multiple modified Riccati equations. In that sense, a single quadratic regulator is used to optimize multiple performance indices. Furthermore, it ensures a minimal guaranteed cost bound over all the performance indices. The proposed approach is illustrated by a numerical example with two quadratic performance objectives.