A Lyapunov-based approach for recursive continuous higher order nonsingular terminal sliding-mode control

A recursive continuous higher-order nonsingular terminal-sliding-mode (TSM) controller is proposed in this paper for nonlinear systems. A new integral TSM manifold is constructed in a recursive manner by modifying the tool of adding a power of integrator instead of exploring nonrecursive design directly. A super-twisting like reaching law is designed to achieve continuous control action without sacrificing disturbance rejection specification as that in boundary-layer approaches. By the new Lyapunov-based design, the proposed control method admits the following new features: 1) rather than imposing some existence condition for nonrecursive design, the proposed method admits the certainty for chosen fractional power to guarantee the finite-time stability of the closed-loop system; 2) an explicit Lyapunov function approach is proposed to establish finite-time stability of the closed-loop system; and 3) The proposed method is shown to be tunable to exhibit desired transient performance and control energy restriction.