Global Control Approach for Nonlinear Systems Contain Delayed States

This scientific research delves into a global control strategy for the pure feedback systems that possess time delay, while also exploring the scenario of nonaffine functions being nondifferentiable. Currently, a majority of the nonaffine pure-feedback systems are transformed into strict feedback function systems by leveraging the mean value theorem, thereby assuming that the nonaffine functions are continuously differentiable. However, this paper introduces the utilization of the median value theorem to reconstruct the nonaffine function, eliminating the requirement for continuous differentiability. By incorporating inverse tangent functions to transform error values, the conventional approach of acquiring the original state in barrier function-based controllers becomes obsolete, allowing for the flexible design of control parameters. As a result, the achievement of global stability in the system is ensured. Additionally, this paper presents a proper Lyapunov-Krasovskii function to handle the presence of a delayed state, enhancing the stability of closed-loop signals. Finally, the simulation provides conclusive evidence regarding the practicality and viability of the proposed schemes in this scholarly paper.