Generalized Super-Twisting for Control Under Time- and State-Dependent Perturbations: Breaking the Algebraic Loop

Application of sliding-mode control strategies based on (generalized) super-twisting (ST) algorithms in the presence of time- and state-dependent perturbations is highly challenging. One of the difficulties lies in the occurrence of a kind of algebraic loop; the bounds required for control design require bounds on the control variable, which itself depends on the control to be designed. Existing results were able to partially solve this problem by means of one form of generalized ST, provided that some perturbation-related functions admit constant bounds. In this article, we provide an important generalization by employing disturbance-tailored ST ideas. The current results allow for far greater applicability, since the bounds required need not be constant as long as their growth can be related to the sliding variable.