Design of an Easy-to-Implement Fixed-Time Stable Sliding Mode Control

This letter introduces a new methodology for the design and tuning of sliding mode controllers with fixed-time stability property for a class of second-order uncertain nonlinear systems. Exploiting the Gauss error function, a novel sliding variable is designed, giving rise to a new control law, whose the main strengths are its ease of implementation and robustness. Indeed, differently from other fixed-time stable techniques in the literature, it only requires the tuning of two design parameters in order to ensure fixed-time convergence, while making the controlled system robust in front of disturbance and uncertainty terms. The properties of the closed-loop systems are theoretically analysed, and the effectiveness of the proposal is shown in simulation on a benchmark example.