Lyapunov函数的可分离性用于收缩单调系统
Separability of Lyapunov Functions for Contractive Monotone Systems
AI总结：
研究了构造同时具有单调性和收缩性的系统Lyapunov函数的方法，提出可分离Lyapunov函数的两种类型，并通过实例展示其应用。
摘要：
我们考虑构造同时具有单调性和收缩性（相对于加权一范数或无穷范数）的系统的Lyapunov函数。此类系统允许可分离的Lyapunov函数，其为单变量函数的和或最大值。无论是哪种情况，都存在两类可分离的Lyapunov函数：一类沿系统状态可分离，另一类沿系统向量场的分量可分离。后者对于许多实际系统更有优势，因为测量系统状态困难，而测量速度或变化率更易实现。我们通过多个示例展示了我们的结果。
英文摘要：
We consider constructing Lyapunov functions for systems that are both monotone and contractive with respect to a weighted one norm or infinity norm. This class of systems admits separable Lyapunov functions that are either the sum or the maximum of a collection of functions of a single argument. In either case, two classes of separable Lyapunov functions exist: the first class is separable along the system's state, and the second class is separable along components of the system's vector field. The latter case is advantageous for many practically motivated systems for which it is difficult to measure the system's state but easier to measure the system's velocity or rate of change. We provide several examples to demonstrate our results.
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