Some mistakes using Lyapunov functions for variable structure control
Abstract
This work discusses some errors found in Lyapunov function proposals of recent results on variable structure control: continuous controllers with finite-time convergence (``Continuous finite-time stabilization of the translational and rotational double integrators'' by Bhat and Bernstein, 1998), based on implicit Lyapunov functions (``Finite-time and fixed-time stabilization: implicit Lyapunov function approach'' by Polyakov et al, 2015), and based on piecewise Lyapunov functions (``An LMI approach for second-order sliding set design using piecewise Lyapunov functions'' Tapia et al, 2017).Downloads
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