On input-output parametric invariance in linear systems

The problem of the invariance of the input-output behavior of time-invariant linear systems under perturbations in the system matrices and initial conditions is examined. Previous results are unified and expanded upon, and new results for invariance in the presence of perturbations in the output matrix are given. Conditions for input-output invariance are related to the subspace of reachable states and its orthogonal complement, and to the subspace of unobservable states.