Construction of ISS Lyapunov functions for Hamiltonian systems with multiple disturbances

In this paper, we proposed a way to construct a ISS Lyapunov function for a class of nonlinear mechanical Hamilton systems with a force disturbance and a velocity disturbance. The construction is based on several assumptions with respect to the system parameters, while those assumptions are easy to be satisfied in practical application. With this result, we can not only make the asymptotic stability analysis of nonlinear pH system easier, but also combine the research result with ISS small gain theorem to discuss the stability of systems in wider area. Copyright (C) 2021 The Authors.