Application of matrix multipliers in case of conic uncertainty sets

The paper determines a guaranteeing cost control for a continuous-time system with generalized positive real uncertainties. Neither the full-block S-procedure technique of [14], nor the result of [2] can be applied in this case, since the uncertainty set is not a subspace, but it is a closed cone only, and the inequality to be investigated is different from that for which the results of [2] are valid. Therefore a new version of the abstract multiplier method is proposed to be used, which is a generalization of the earlier multiplier methods. This application illustrates that the abstract multiplier method enlarges the class of robust control problems that can be treated by linear matrix inequalities.