SMC for nonlinear systems with mismatched uncertainty using Lyapunov-function integral sliding mode

In this paper, the mismatched uncertainty and disturbance rejection is addressed for uncertain nonlinear systems by a class of integral sliding mode (ISM) design. First, after describing the system control problem, the ISM design problem is given. Then, two kinds of ISM are presented that have the ability to reject the mismatched uncertainty and disturbance. One is called Lyapunov-function integral sliding mode (LFISM) and the other is called assistant-Lyapunov-function integral sliding mode (ALFISM). The system state in the ideal sliding mode of the two ISM surfaces is proved to be robustly stable despite the existence of the mismatched uncertainty and disturbance. In the presented framework, a general case of single input nonlinear system was studied and verified by a simulation application to a one-link robotic manipulator. Additionally, applications to a unicycle using the ISM with the mismatched-disturbance minimisation (ISM-MDM) method, the high-order disturbance observer (HODO) technique, and the LFISM method were reported. The simulation results confirmed that the LFISM's rejection effect to the mismatched disturbance is better.