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.