On the sensitivity of linear state-space systems

Abstract

This paper contains new measures to describe the transfer function sensitivity of state-space systems with respect to value and parameter perturbations. These measures are related to the newly defined generalized Gramian matrices. The value respecting the parameter variations contains the sensitivity at discrete frequency points, pole and zero sensitivities and the integral sensitivity as special cases. A general relation to the variance of the weighted output noise can be obtained in the case of a perturbed realization which is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l_2</tex> -scaled under a general non-white input process. The complete class of representations with minimum sensitivity and noise is given. The corresponding necessary and sufficient conditions lead to an analytic design of optimal state-space systems.