A Sliding Mode Control Method With Variable Convergence Rate for Nonlinear Impulsive Stochastic Systems

This article addresses the variable convergence rate stability problem for nonlinear impulsive stochastic systems (NISSs). To solve the issue, a novel methodology of sliding mode surface design is presented by combining the definition of interval stability with the T-S fuzzy technique. A pioneering class of sliding mode controllers is constructed in accordance with the characteristics of the designed sliding mode surfaces and the sigmoid function. These controllers can intelligently adjust the convergence rate of the system according to practical requirements, thereby addressing the limitation of fixed convergence rate in existing results. Moreover, the proposed controllers can effectively suppress jitter and analyze the effects of different sigmoid functions on jitter suppression. Sufficient conditions are derived to ensure that the states of the NISSs reach the designed surfaces in finite time and to achieve variable convergence rate stability. The excellent performance of the proposed theoretical strategy in achieving adjustable rate convergence of the system is demonstrated through a simulation of the ball-beam system.