Finite time terminal sliding mode control for a class of time delay systems

A fast terminal sliding mode controller is proposed for a class of linear systems with distributed delays in state and control variables. By properly designing a state transformation and a predictor, the given system can be changed into a time-delay free. The proposed terminal sliding manifold is given using the recursive mechanism. It is shown that by suitably choosing the parameters of the fast terminal sliding modes, system state variables would reach the fast terminal sliding manifold within a desired finite time and stay there forever, resulting in the convergence to equilibrium in a finite time. The global stability of the closed-loop system is guaranteed and the singularity problem usually existed in the terminal sliding mode control is avoided. Although the proposed control strategy is sliding mode based, the control signal is continuous except at a single discontinuous point. Chattering phenomenon commonly associated with sliding mode control does not occur.