Simplification in the computation of the sensitivity functions for constant coefficient linear systems

It is often necessary to compute the sensitivity functions for system parameters and initial conditions in a dynamic system. In this paper, it is shown that for constant coefficient linear systems all possible sensitivity functions can be obtained by linear transformations on the solutions to th-order differential equations, where is the number of independent inputs to the system, and is the minimal order realization for the system. The transformations required to obtain the output sensitivities for a single-output multi-input system, which is modeled in a companion form, reduce to the identity.