A linear framework for the robust stability analysis of a Generalized Super-Twisting Algorithm

In this paper a linear framework is proposed for the analysis and design of stable and robust stable Generalized Super-Twisting Algorithms (GSTA). The GSTA includes a linear version of the algorithm, the standard STA and a STA with extra linear correction terms, that provide more robustness and convergence velocity. This linear framework allows to construct strong Lyapunov functions of quadratic-like type for the GSTA by means of Algebraic Lyapunov Equations (ALE), in exactly the same form for the linear STA and for the GSTA. When nonlinear perturbations are present this framework leads to the construction of robust Lyapunov functions by solving Algebraic Riccati Inequalities (ARI) or Linear Matrix Inequalities (LMI), that are identical for the linear and the nonlinear versions of the GSTA. The corresponding frequency domain interpretations are also identical for the whole class of GSTA.