Performance robustness analysis of sampled-data systems against control-input matrix uncertainties

In this paper, we present a result that allows the computation of the worst-case quadratic performance for a class of linear time-invariant sampled-data systems that depend on a real constant parametric uncertainty. The sampled-data systems result from using a discrete-time regulator for the feedback control of an analog plant. The plant is itself described by a state-space model where the control-input matrix has an affine linear dependence on the uncertain parameter. The results of this paper have potential application in situations where actuators introduce parametric uncertainties, and in computing gain margins. We show that the computation of the worst-case quadratic performance is similar to that of the H∞ norm of a certain system, whose state-space realization can be constructed from the data. This is due to the rational dependence of the quadratic norm on the uncertain parameter