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Incremental stability of Lur’e systems through piecewise-affine approximations

机译：通过分段仿射逼近的Lur'e系统的增量稳定性

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摘要

Lur’e-type nonlinear systems are virtually ubiquitous in applied control theory, which explains the great interest they have attracted throughout the years. The purpose of this paper is to propose conditions to assess incremental asymptotic stability of Lur’e systems that are less conservative than those obtained with the incremental circle criterion. The method is based on the approximation of the nonlinearity by a piecewise-affine function. The Lur’e system can then be rewritten as a so-called piecewise-affine Lur’e system, for which sufficient conditions for asymptotic incremental stability are provided. These conditions are expressed as linear matrix inequalities (LMIs) allowing the construction of a continuous piecewise-quadratic incremental Lyapunov function, which can be efficiently solved numerically. The results are illustrated with numerical examples.
机译：Lur'e型非线性系统在应用控制理论中几乎无处不在，这说明了它们多年来引起的极大兴趣。本文的目的是提出评估Lur’e系统增量渐近稳定性的条件，这些条件不如采用增量圆准则获得的渐进稳定性好。该方法基于分段仿射函数对非线性的近似。然后可以将Lur’e系统改写为所谓的分段仿射Lur’e系统，为此提供了足够的渐近渐进稳定性条件。这些条件表示为线性矩阵不等式（LMI），可以构造连续的分段二次增量Lyapunov函数，可以有效地对其进行数值求解。结果用数值例子说明。

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