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Conference Papers Year : 2011

Numerical construction of LISS Lyapunov functions under a small gain condition

Fabian Wirth
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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.

Dates and versions

hal-00724979 , version 1 (23-08-2012)

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Cite

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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