Robust controller synthesis for plants satisfying a certain class of IQC

This paper considers robust stabilization problem for plants with uncertainties/nonlinearities satisfying a certain class of integral quadratic constraints (IQCs). The restricted class of IQCs can still characterize many kinds of uncertainties/nonlinearities. We show that this problem reduces to the feasibility of nonconvex matrix inequalities. Owing to their special structure, they can be solved with reasonable computational effort - which is not the case with bilinear matrix inequalities (BMIs) - by combining a nonconvex optimization technique with an interior-point methodology to solve linear matrix inequalities (LMIs). Finally, an illustrative numerical example is given, where the proposed approach is applied to achieve specified gain and phase margins