ABSTRACT
This chapter aims to demonstrate a design method for discontinuous control enforcing sliding mode in some manifold without individual selection of each component of control as a discontinuous state function. The approach implies design of control based on a Lyapunov function selected for a nominal system. Decoupling is feasible because the sliding mode equations do not depend on control but they do depend on the sliding manifold equation. The control is to be found such that the time derivative of the Lyapunov function is negative along the trajectories of the system with perturbations caused by uncertainties in the plant model and environment conditions. In numerous publications, different design methods were offered for these cases, and the authors referred to these methods as “high-order sliding mode control.” Similar to the twisting algorithm, the super-twisting sliding mode control algorithm relies on inserting an integrator into the control loop, such that control becomes a continuous time function.
