Stability analysis of a cart-pendulum model with variable convergence rate: A sliding mode control approach for impulsive stochastic systems

In this paper, a sliding mode control problem with variable convergence speed for impulsive stochastic systems based on the cart-pendulum model is investigated. Firstly, the cart-pendulum is modeled as impulsive stochastic system and the interval-driven stability criterion for variable convergence rate is given according to the idea of pole configuration. Meanwhile, the corresponding sliding mode surface functions are designed by pre-adjusting the intervals which in turn regulate the convergence rate of the target system states. To attenuate the oscillation phenomenon that exists in the sliding mode control, the new continuous control rate function is designed on the basis of the saturation function. In addition, a sliding mode control strategy for impulsive stochastic systems is presented to ensure the reachability of the designed sliding surface in finite time and the stability of the reduced-order system under motion of the sliding mode. Finally, the cart-pendulum simulation results demonstrate the effectiveness and feasibility of the sliding mode control.