Sensitivity integrals and transformation techniques: a new perspective

In this paper 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-transforms. 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