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Numerical construction of LISS Lyapunov functions under a small gain condition

Abstract : We provide a homotopy algorithm that computes a decay point of a monotone operator, i.e., a point whose image under the monotone operator is strictly smaller than the preimage. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. This decay point plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system numerically and in the numerical construction of local input-to-state stability (LISS) Lyapunov functions. We give some improvements of this algorithm and show the advantage to an earlier approach based on the algorithm of Eaves.
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https://hal.inria.fr/hal-00724979
Contributor : Estelle Bouzat <>
Submitted on : Thursday, August 23, 2012 - 3:03:13 PM
Last modification on : Friday, September 17, 2021 - 2:50:09 PM

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Roman Geiselhart, Fabian Wirth. Numerical construction of LISS Lyapunov functions under a small gain condition. 50th IEEE Conference on Decision and Control, 2011, Orlando, United States. pp.6967-6972, ⟨10.1109/CDC.2011.6160908⟩. ⟨hal-00724979⟩

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