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Continuous and Piecewise Affine Lyapunov Functions using the Yoshizawa Construction

Abstract : We present a novel numerical technique for the computation of a Lyapunov function for nonlinear systems with an asymptotically stable equilibrium point. Our proposed approach constructs a continuous piecewise affine (CPA) function given a suitable partition of the state space, called a triangulation, and values at the vertices of the triangulation. The vertex values are obtained from a Lyapunov function in a classical converse Lyapunov theorem and verification that the obtained CPA function is a Lyapunov function is shown to be equivalent to verification of several simple inequalities. Furthermore, by refining the triangulation, we show that it is always possible to construct a CPA Lyapunov function. Numerical examples are presented demonstrating the effectiveness of the proposed method.
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https://hal.inria.fr/hal-00944393
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Submitted on : Monday, February 10, 2014 - 3:30:29 PM
Last modification on : Friday, August 23, 2019 - 3:08:02 PM
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Sigurđur Freyr Hafstein, Christopher M. Kellett, Huijuan Li. Continuous and Piecewise Affine Lyapunov Functions using the Yoshizawa Construction. American Control Conference (ACC), 2014, 2014, Portland, United States. pp.548 - 553, ⟨10.1109/ACC.2014.6858660⟩. ⟨hal-00944393⟩

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