Dynamics Analysis of Discrete-time Sliding Mode Controller for the Nonlinear Systems

This brief research proposes a discrete-time sliding mode controller and studies its dynamic characteristics. First, this research develops a discrete-time sliding mode reaching law by redefining the change rate of disturbance through difference function, estimating disturbances using disturbance estimation techniques and compensating them into the reaching law, and further designing a discrete-time sliding mode controller. Second, through theoretical analysis, the width of quasi-sliding mode domain(QSMD), and convergence steps are obtained, and the bounded convergence property of system state variables is proven. Lastly, the correctness of the theoretical analysis and effectiveness of the controller are verified through simulations. Simulation results demonstrate that the proposed controller can ensure that the switching function reaches QSMD within a finite time and continue to move within QSMD, and the system state will eventually converge.