Tracking in a class of nonlinear differential inclusion systems by finite-reaching time sliding mode control

In this paper, tracking problem in nonlinear polytopic differential inclusion systems in the presence of input nonlinearities and bounded disturbances is investigated. The input nonlinearities are assumed to be sector nonlinearity or dead-zone nonlinearity. A sliding mode controller is proposed to achieve the tracking for the mentioned differential inclusion systems in finite time. The suggested control approach is composed of sliding surfaces and control inputs. Based on Lyapunov stability theorem it is proved that the considered inclusion systems with the designed control inputs can track desired trajectories in finite time. Finally, two numerical simulations are provided to verify the effectiveness of proposed control approach.