Summary: The finite-time stabilization and \(H_\infty\) control of stochastic nonlinear systems was investigated in this article. First, we discussed the relationship between the finite-time stability and the dissipation property by transforming the stochastic nonlinear system to its equivalent Hamiltonian formulation. It was showed that the stochastic dissipative Hamiltonian system is finite-time stable in probability if the system is strictly dissipative and the Hamiltonian function possessed some special forms. Then, by the energy shaping and damping injection technique, we reformulate the internal structure matrix and the Hamiltonian function to construct a finite-time stabilization controller for stochastic nonlinear systems. Moreover, for uncertain stochastic nonlinear systems, an \(H_\infty\) finite-time robust controller was put forward by utilizing the Hamiltonian function to construct a solution for the Hamiltonian-Jacobi Inequality. Finally, we proposed a finite-time stabilization and a finite-time \(H_\infty\) controller for the inverted cart-pendulum system to verify the effectiveness of the proposed method.
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