We investigate the problem of asymptotic stability for nonstationary switched systems. The direct Lyapunov method is used. It is assumed that for any mode a comparison equation in the Bernoulli form is constructed for the considered system. Sufficient conditions on the nonstationary coefficients of the comparison equations and the switching law are found to guarantee the asymptotic stability of the zero solution of the studied system. Obtained results are applied to the stability analysis of some classes of mechanical systems with switched force fields.

中文翻译：

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非平稳切换系统的稳定性分析

我们研究了非平稳切换系统的渐近稳定性问题。使用直接李雅普诺夫方法。假定对于任何模式，针对所考虑的系统都构造了伯努利形式的比较方程。发现比较方程的非平稳系数和切换定律的充分条件，以保证所研究系统零解的渐近稳定性。所得结果可用于某些类别具有切换力场的机械系统的稳定性分析。