Robust Performance Analysis for Structured Linear Time-Varying Perturbations With Bounded Rates-of-Variation

The robust performance analysis problem is considered for linear time-invariant (LTI) systems subject to block-diagonal structured and bounded linear time-varying (LTV) perturbations with specified maximal rates-of-variation. Analysis methods are developed in terms of semidefinite programming for the computation of upper and lower bounds for the optimum robust performance level. The upper bound computation is based on an integral quadratic constraint (IQC) test developed using a generalized version of the so-called swapping lemma. The lower bound computation method employs an extended version of the power distribution theorem together with a generalized version of the Kalman-Yakubovich-Popov (KYP) lemma and serves as a means to assess the conservatism of the computed upper bounds in the case of dynamic LTV perturbations. As corollaries of the underlying result for lower bound computation, it is shown for general block-diagonal uncertainty structures that thefrequency-dependent/constant D-scaling tests are exact for robust performance analysis against arbitrarily slow/fast dynamic LTV perturbations, respectively