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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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1573-269X

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On stability analysis via Lyapunov exponents calcu

Authors: Caixia Yang Qiong Wu
Publish Date: 2009/06/04
Volume: 59, Issue: 1-2, Pages: 239-
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Abstract

The concept of Lyapunov exponents has been mainly used for analyzing chaotic systems where at least one exponent is positive The methods for calculating Lyapunov exponents based on a time series have been considered not reliable for computing negative and zero exponents which prohibits their applications to potentially stable systems It is believed that the local linear mapping leads to inaccurate matrices which prevent them from calculating negative exponents In this work the nonlinear approximation of the local neighborhoodtoneighborhood mapping is derived for constructing more accurate matrices To illustrate the approach the Lyapunov exponents for a stable balancing control system of a bipedal robot during standing are calculated The time series is generated by computer simulations Nonlinear mapping is constructed for calculating the whole spectrum of Lyapunov exponents It is shown that as compared with those from the linear mapping 1 the accuracy of the negative exponents calculated using the nonlinear mapping is significantly improved 2 their sensitivity to the time lag and the evolution time is significantly reduced and 3 no spurious Lyapunov exponent is generated if the dimension of the state space is known Thus the work can contribute significantly to stability analysis of robotic control systems Issues on extending the concept of Lyapunov exponents to analyzing stable systems are also addressed

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