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
(p + 2) n
th-order differential equations, where
p
is the number of independent inputs to the system, and
n
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.