Lyapunov-based Methods for Maximizing the Domain of Attraction
Keywords:
Lyapunov function, nonlinear model, asymptotic stability, equilibrium point, genetic algorithm, threshold accepted algorithm, LMIAbstract
This paper investigates Lyapunov approaches to expand the domain of attraction (DA) of nonlinear autonomous models. These techniques had been examined for creating generic numerical procedures centred on the search of rational and quadratic Lyapunov functions. The outcomes are derived from all investigated methods: the method of estimation via Threshold Accepted Algorithm (TAA), the method of estimation via a Zubov technique and the method of estimation via a linear matrix inequality (LMI) optimization and genetic algorithms (GA). These methods are effective for a large group of nonlinear models, they have a significant ability of improvement of the attraction domain area and they are distinguished by an apparent propriety of direct application for compact and nonlinear models of high degree. The validity and the effectiveness of the examined techniques are established based on a simulation case analysis. The effectiveness of the presented methods is evaluated and discussed through the study of the renowned Van der Pol model.
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