Cascaded-based stabilization of time-varying systems using second-order sliding modes

We present a result on stabilization of strict feedback systems with unknown disturbances based on the so-called twisting algorithm, a second-order sliding mode controller for the double integrator. The novelty of the note relies in the stability analysis of the closed-loop system and the relaxation of stability conditions (we do not assume boundedness of trajectories). The proof of the main result is constructed along similar lines as for well-established theorems for nonlinear time-varying systems in cascade, with continuous right-hand sides. Although we restrict our analysis to second-order systems, the purpose of this note is to settle the basis for a methodological stability analysis approach for higher-order systems in strict feedback form, under the influence of uncertain perturbations. An illustrative example is provided.