In this article the polynomial stability for positive switching homogeneous systems with different degrees is investigated by proposing a logarithm contraction average dwell-time method. By introducing a class of logarithm contraction average dwell-time switching signals and a piecewise maximum Lyapunov function, we establish an explicit criterion for global polynomial stability of positive switching homogeneous systems whose degrees are greater than one. Especially, the main result is applicable to polynomial stability of Persidskii-type switching systems and consensus of multi-agent systems.

中文翻译：

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不同阶正切换齐次系统的多项式稳定性

在本文中，通过提出对数收缩平均停留时间方法，研究了不同阶正切换齐次系统的多项式稳定性。通过引入一类对数收缩平均驻留时间切换信号和分段最大李雅普诺夫函数，我们建立了度数大于1的正切换齐次系统全局多项式稳定性的显式判据。特别是，主要结果适用于 Persidskii 型交换系统的多项式稳定性和多智能体系统的一致性。