Bounded stabilisation of stochastic port-Hamiltonian systems

This paper proposes a stochastic bounded stabilization method for a class of stochastic port-Hamiltonian systems. Both full-actuated and underactuated mechanical systems in the presence of noise are considered in this class. The proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability. The bounded region and achieving probability are both assignable, and a stochastic Lyapunov function is explicitly provided based on a Hamiltonian structure. Although many conventional stabilization methods assume that the noise vanishes at the origin, the proposed method is applicable to systems under persistent disturbances.