Computation of Lyapunov Functions for Discrete-Time Systems using the Yoshizawa Construction

Abstract : In this paper, we present a new approach for com-puting Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. The pro-posed method constructs a continuous piecewise affine (CPA) function on a compact subset of the state space containing the origin, given a suitable triangulation or partition of the compact set and values at the vertices of the triangulation. Here, the vertex values are fixed using a function from a classical con-verse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.
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Communication dans un congrès
CDC 2014, Dec 2014, Los Angeles, United States. Proceedings of the 53rd IEEE Conference on Decision and Control. 〈http://control.disp.uniroma2.it/CDC2014/〉
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Huijuan Li, Sigurður Hafstein, Christopher M. Kellett. Computation of Lyapunov Functions for Discrete-Time Systems using the Yoshizawa Construction. CDC 2014, Dec 2014, Los Angeles, United States. Proceedings of the 53rd IEEE Conference on Decision and Control. 〈http://control.disp.uniroma2.it/CDC2014/〉. 〈hal-01101289〉

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