New observer-based stabilization method for stochastic Hamiltonian systems with time-varying delay

This paper considers the stabilization problem of nonlinear stochastic Hamiltonian systems with input time-varying delay. The systems under consideration are also subject to some small parameter perturbations in which are unavoidably involved. The dissipative structural properties of the Hamiltonian systems are fully considered and an observer-based adaptive controller are proposed to guarantee robustly asymptotically stable in mean square of the closed-loop systems for all admissible uncertainties, as well as bounded delay. Augmented Lyapunov-Krasovskii functionals are constructed and Wirtinger inequalities are utilized to estimate the derivatives of the candidate Lyapunov functionals more accurately. Numerical simulation spells out to illustrate the effectiveness and less conservatism of the proposed method.