A Formal Proof of Two Properties of Laplace Transform

In our previous work, we have introduced a formal definition of Laplace transform in Coq, and proved a group of basic properties of Laplace transform, including linear property, frequency shifting and first order differentiation. However, in many control systems, Laplace transforms are often applied on functions containing second-order derivatives and integrals with variable upper bound. This paper extends our previous results by adding formal Coq proofs on properties of these two kinds of Laplace transforms. Finally, as an application of these formal properties, we presents a formal derivation of the transfer function of a DC motor control system for robots.