AI 中文总结
研究二维切换齐次系统在任意切换下的稳定性，用最坏情况切换分析证明充要条件。基于此研究切换线性系统原点稳定性分岔，得出非线性切换系统相关稳定性结果，还制定了方法确定一类系统有界吸引域的存在。
AI 中文摘要
我们利用最坏情况切换分析，证明了具有有限个子系统的二维切换齐次系统在任意切换下一致渐近稳定的新的充要条件。我们方法的新颖之处在于其显式性质，这使我们能够详细研究切换线性系统中原点稳定性的余维一分岔，并进一步得出某些类非线性切换系统的新的局部和全局稳定性结果。特别是，我们为\(\mathcal{C}^{1}\)切换非线性系统制定了李雅普诺夫间接方法的类似方法，并推导了一种确定一类切换非线性系统存在有界吸引域的新方法。
英文摘要
We prove new necessary and sufficient conditions for uniform asymptotic stability under arbitrary switching of two-dimensional switched homogeneous systems with a finite number of subsystems using a worst-case switching analysis. The novelty of our approach is in its explicit nature, which allows us to then study in detail the codimension-one bifurcations of stability of the origin in switched linear systems and further conclude new local and global stability results for certain classes of nonlinear switched systems. In particular, we formulate an analogue of Lyapunov's indirect method for $\mathcal{C}^{1}$ switched nonlinear systems and derive a new method for determining the existence of a bounded basin of attraction for a class of switched nonlinear systems.
Comments44 pages, 3 figures
