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Journal Articles Mathematics of Control, Signals, and Systems Year : 2012

Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition

Abstract

In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. This decay point plays a crucial role in numerically checking small gain conditions that guarantee the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone operator. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. The advantage to an earlier algorithm due to Eaves is demonstrated. Furthermore an example is given which shows how to analyze a given perturbed interconnected system.

Dates and versions

inria-00636097 , version 1 (26-10-2011)

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Cite

Roman Geiselhart, Fabian R. Wirth. Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition. Mathematics of Control, Signals, and Systems, 2012, 24 (1-2), pp.3-32. ⟨10.1007/s00498-012-0082-2⟩. ⟨inria-00636097⟩
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