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Co-Positive Lyapunov Functions for the Stabilization of Positive Switched Systems

机译：正正开关系统稳定的共正Lyapunov函数

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摘要

In this paper, exponential stabilizability of continuous-time positive switched systems is investigated. For two-dimensional systems, exponential stabilizability by means of a switching control law can be achieved if and only if there exists a Hurwitz convex combination of the (Metzler) system matrices. In the higher dimensional case, it is shown by means of an example that the existence of a Hurwitz convex combination is only sufficient for exponential stabilizability, and that such a combination can be found if and only if there exists a smooth, positively homogeneous and co-positive control Lyapunov function for the system. In the general case, exponential stabilizability ensures the existence of a concave, positively homogeneous and co-positive control Lyapunov function, but this is not always smooth. The results obtained in the first part of the paper are exploited to characterize exponential stabilizability of positive switched systems with delays, and to provide a description of all the “switched equilibrium points” of an affine positive switched system.
机译：本文研究了连续时间正切换系统的指数稳定性。对于二维系统，当且仅当存在（梅茨勒）系统矩阵的Hurwitz凸组合时，才可以通过开关控制定律实现指数稳定。在更高维的情况下，通过一个例子表明，Hurwitz凸组合的存在仅足以实现指数稳定，并且只有当存在光滑，正均质且协调的情况时，才能找到这种组合。 -正控制系统的Lyapunov功能。在一般情况下，指数稳定性可确​​保存在凹形，正均匀且共正控制的Lyapunov函数，但这并不总是很平稳。本文第一部分中获得的结果被用来刻画具有正时滞的正切换系统的指数稳定性，并提供了仿射正切换系统的所有“切换平衡点”的描述。

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