Conditions for boundedness of under-tuned super-twisting sliding mode control loops

This study investigates the behaviour of super-twisting sliding-mode control loops that are subject to a class of bounded-rate perturbations when the established conditions for (FTS) do not hold. The motivation for this consideration is that oftentimes imposing the FTS conditions, i.e. requiring that the integral gain of the controller be larger than the total perturbation derivative, can be very restrictive in relation to actuator limitations. It is proven that under milder conditions for the control gains, the trajectories of the under-tuned closed-loop system are (UGUB) in a domain containing the origin. The result holds for both periodic perturbations of arbitrarily large period and bounded-mean oscillatory perturbations.