Finite/fixed-time practical sliding mode: An event-triggered approach

This paper proposes a unified event-triggered sliding-mode control framework to attain the finite/fixed-time reachability of practical sliding-mode band. In event-triggered sliding-mode control, the practical sliding mode makes the size of the sliding-mode band dependent on the event function rather than the disturbance bound and sampling interval and provides better control performance due to this advantage. Under this paper's unified framework, the predesigned practical sliding-mode band can be respectively reached within a finite/fixed time by choosing different parameters. Then, different from the asymptotical convergence obtained in other investigations, the ultimate finite-time stability of the controlled system can be guaranteed. In the sliding phase, by adjusting the initial value of integration for settling time from initial value of the controlled system to the point where the sliding phase starts, a more precise estimation to settling time is obtained and can be generalized to different kinds of systems. In addition, in comparison to other results in finite-time event-triggered sliding-mode control, signum function is subtracted from the measurement error which eliminates the Zeno phenomenon and ensures the reliable operation of the digital controller in reality. Finally, a numerical example is given to verify the effectiveness of the theoretical results.