On fast terminal sliding-mode control design for higher order systems

This manuscript discusses a new algorithm for finite time convergence of the states for a higher order system. To this end, a set of fast terminal sliding mode surfaces are constructed. The fractional powers of the switching surfaces are selected such that singularity is avoided during sliding. A control signal is developed with necessary and sufficient conditions for the finite time convergence is obtained, under which the system states reach the fast terminal sliding surfaces in a finite time and stay in the sliding modes thereafter. A condition on external disturbance is obtained to guarantee the finite time convergence. Numerical simulations are provided to validate the theoretical results and examine the robustness of control against external disturbances.