Observer-Based Fuzzy Sliding Mode Control Approach For Uncertain Underactuated Nonlinear Systems With Time Delay

In this paper, an observer-based fuzzy sliding mode control approach for uncertain underactuated nonlinear systems with time delay is proposed. This study deals with the problem of controlling a class of uncertain nonlinear systems in the presence of the state time delay. The fuzzy logic systems are used to approximate the unknown nonlinear functions by some adaptive laws, and a fuzzy state observer is employed to estimate the unmeasured states. A stability criterion in terms of Lyapunov-Krasovskii functional method is derived to guarantee the stability of uncertain underactuated nonlinear systems with state time delay. From Lyapunov stability theorem, the proposed design approach can not only guarantee semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system, but also converge to a small neighborhood of the origin for the tracking error of the system. Finally, the simulation results are given to show the effectiveness of the proposed control approach.