Tractable Approximations of LMI Robust Feasibility Sets

In this letter, we introduce novel tractable approximations for robust Linear Matrix Inequality (LMI) problems. We present various Quadratic Matrix Inequalities (QMIs) that enable us to characterize the effect of ellipsoidal uncertainty in the robust problem. These formulations are expressed in terms of a set of auxiliary decision variables, which facilitate the derivation of a generalized S-procedure result. This generalization significantly reduces the conservatism of the obtained results, compared with conventional approaches.