Abstract
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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(p + 2) n</tex> th-order differential equations, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> is the number of independent inputs to the system, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> 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.
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