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首页> 外文期刊>IEEE Transactions on Automatic Control >Regions of Stability for Limit Cycle Oscillations in Piecewise Linear Systems
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Regions of Stability for Limit Cycle Oscillations in Piecewise Linear Systems

机译：分段线性系统极限环振动的稳定性区域

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Oscillations appear in numerous applications from biology to technology. However, besides local results, rigorous stability and robustness analysis of oscillations are rarely done due to their intrinsic nonlinear behavior. Poincare maps associated with the system cannot typically be found explicitly and stability is estimated using extensive simulations and experiments. This paper gives conditions in the form of linear matrix inequalities (LMIs) that guarantee asymptotic stability in a reasonably large region around a limit cycle for a class of systems known as piecewise linear systems (PLS). Such conditions, based on recent results on impact maps and surface Lyapunov functions (SuLF), allow a systematic and efficient analysis of oscillations of PLS or arbitrarily close approximations of nonlinear systems by PLS. The methodology applies to any locally stable limit cycle of a PLS, regardless of the dimension and the number of switching surfaces of the system, and is illustrated with a biological application: a fourth-order neural oscillator, also used in many robotics applications such as juggling and locomotion.
机译：振荡出现在从生物学到技术的众多应用中。但是，除了局部结果外，由于其固有的非线性行为，很少对振动进行严格的稳定性和鲁棒性分析。通常无法明确找到与系统关联的Poincare图，并且使用大量的模拟和实验来评估稳定性。本文给出了线性矩阵不等式（LMI）形式的条件，这些条件可保证在称为分段线性系统（PLS）的一类系统的极限环附近的合理较大区域中的渐近稳定性。基于冲击图和表面Lyapunov函数（SuLF）的最新结果，这些条件允许对PLS的振荡或PLS非线性系统的任意近似近似进行系统而有效的分析。该方法适用于PLS的任何局部稳定极限周期，而与系统的切换表面的尺寸和数量无关，并已在生物学应用中进行了说明：四阶神经振荡器，也用于许多机器人应用中，例如玩杂耍和运动。

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