Formalization of Laplace Transform Using the Multivariable Calculus Theory of HOL-Light

Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems. To facilitate formal analysis of these systems, we present the formalization of Laplace transform using the multivariable calculus theories of HOL-Light. In particular, we use integral, differential, transcendental and topological theories of multivariable calculus to formally define Laplace transform in higher-order logic and reason about the correctness of Laplace transform properties, such as existence, linearity, frequency shifting and differentiation and integration in time domain. In order to demonstrate the practical effectiveness of this formalization, we use it to formally verify the transfer function of Linear Transfer Converter (LTC) circuit, which is a commonly used electrical circuit.