Robust performance analysis for systems with norm-bounded time-varying structured uncertainty

This paper analyses robust performance measures for linear time-invariant systems with norm-bounded time-varying structured uncertainty. We consider two robust performance measures. One is the worst case peak value of the error signal in response to the disturbance with a known energy. The other is the worst case energy of the error signal in response to impulsive disturbance. In both cases, the "worst case" is taken over all admissible uncertainties and disturbances. The notion of robust stability is Q-stability, or the scaled H_∞, norm bound. Our main results provide an upper bound for each of the robust performance measures in terms of a positive definite matrix which satisfies a linear matrix inequality (LMI) together with a scaling matrix. Hence, the best bound in this LMI formulation can be computed by convex programming.