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Publication Detail
A unified lyapunov function for finite time stabilization of continuous and variable structure systems with resets
© Springer International Publishing AG 2018. A unilaterally constrained perturbed double integrator system is studied in this work. The aim is to establish uniform finite time stability of the non-linear dynamics in the presence of impacts due to the constraints on the position variable. A non-smooth transformation is utilized to first transform the system into a variable structure system that can be studied within the framework of a conventional discontinuous paradigm. Then, a finite time stable continuous controller is used and stability of the closed-loop dynamics is proven by identifying a new set of Lyapunov functions. The results enable continuous and discontinuous cases to be unified using one parameter that defines the set of Lyapunov functions for each case.
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