Design of fixed-time sliding mode control using variable exponents

This paper proposes the design of a robust fixed-time sliding mode controller for a second-order nonlinear system with matched and unmatched uncertainties. First, a fixed-time stable scalar dynamics with a variable exponent is introduced. We establish the global fixed-time stability results for the proposed dynamics using Lyapunov analysis. The maximum convergence time has been derived in terms of the design parameters, which is independent of the initial conditions. These results are then extended to solve the robust fixed-time stabilization for uncertain nonlinear second-order system. Specifically, we proceed with the sliding mode control design, where the sliding surface and the control law are motivated by the proposed scalar dynamics. Moreover, the proposed design is free from singularity and guarantees fixed-time robust stabilization. Simulation results with comparative analysis has been included. Further, experimental validation on a single link manipulator is provided to demonstrate the performance of the proposed approach.