Matrix calculus and the sensitivity analysis of linear dynamic systems

The formulas for the derivatives of state transition matrices [3], [8] are extended in this note. The great usefulness of the matrix calculus [10], [12] is then demonstrated with alternative derivations of results in the theory of sensitivity analysis [8], [14] which are shorter and simpler than the original developments. It is anticipated that the formulas derived herein will be applied to parameter identification and feedback design methodologies.