Almost sure stability of second‐order nonlinear stochastic system with Lévy noise via sliding mode control

Summary The almost sure stability of second‐order nonlinear stochastic system with Lévy noise is studied by sliding mode control method. A conventional linear sliding mode surface is first constructed, by employing stochastic analysis technique combined with Lyapunov function method, sufficient conditions are established to ensure the almost sure stability of the system dynamics. Then, a nonsingular terminal sliding mode control technique is used for our system, corresponding controller is designed to guarantee the desired performance. Finally, two examples are given to show the validity of our results.