Lyapunov stability analysis of a twisting based control algorithm for systems with unmatched perturbations

In this note, we present a result on stabilization of nonlinear strict-feedback systems affected by unknown perturbations when a control based on the so-called twisting algorithm, a second-order sliding mode controller, is applied. The novelty of the note relies in the stability analysis of the closed loop system. It follows along similar lines as for well-established theorems for nonlinear time-varying systems in cascade, with continuous right-hand sides. However, the class of systems that we deal with are discontinuous and perturbed. Although the presented analysis is aimed to perturbed second-order systems in strict feedback form, the purpose of this note is to settle the basis for a methodological stability analysis approach for higher-order systems. An illustrative example is provided.