Sensitivity integrals and transformation techniques: a new perspective

We provide alternative proofs for the classical Bode and Poisson-type sensitivity integrals and their extensions for both continuous-time and discrete-time systems. Our derivation uses the well-known properties of Laplace and Z transformations. This derivation helps establish a connection between Bode and Poisson-type sensitivity integrals and Laplace and Z transforms, hence providing an alternative perspective in interpreting these fundamental integral results.