The problem of generating the state sensitivity functions of linear time-invariant continuous systems using only one additional cascaded model having the same dimension as that of the system is treated in this paper. Necessary and sufficient conditions for the state sensitivity functions to be expressed as linear transformations of the combined state of the system and the cascaded model are derived. Explicit expressions for these linear transformations are obtained via the necessary and sufficient conditions for the controllable and alpha canonical forms, both with single input.