Free-will Arbitrary Time Terminal Sliding Mode Control

In this technical note, free-will arbitrary time terminal sliding mode control design is proposed. With such a design, it is possible to control the time duration of sliding in the sliding phase. Under the assumption that the chosen arbitrary time is greater than the reaching phase time (tr), it is shown that the nth order chain of integrators converges to zero within the selected arbitrary time. An algorithm is also proposed for the case when tr is not known to the designer. Stability analysis based on Lyapunov theory has been provided.