A general form and improvement of fast terminal sliding mode

This paper presents a general form for the fast terminal sliding mode (FTSM). It is shown that the proposed form not only includes the conventional FTSM, but also provides new types of FTSM which can have a faster convergence rate than the conventional one. More importantly, the convergence time of the new FTSM models is bounded for any initial value, which means an upper bound of the convergence time that is determined only by parameters can be obtained. Therefore, when using the new FTSM models in the control of higher order systems, the systems can be stabilized in a certain time which can be designed and estimated out-line. Finally, the improved FTSM (IFTSM) models are applied in design of the sliding mode control for single-input single-output (SISO) nonlinear systems with uncertainty and external disturbance.