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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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Submitted on : Friday, July 18, 2014 - 3:49:38 PM
Last modification on : Friday, September 17, 2021 - 2:50:09 PM
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  • HAL Id : hal-01025882, version 1



Huijuan Li, Sigurđur Hafstein, Christopher M. Kellett. Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction. NETCO 2014 - New Trends in Optimal Control, Jun 2014, Tours, France. ⟨hal-01025882⟩



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