A note on stability conditions for planar switched systems
A note on stability conditions for planar switched systems
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DOI：
10.1080/00207170902802992
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发表时间：
2008-09
影响因子：
2.1
通讯作者：
M. Balde;U. Boscain;P. Mason
中科院分区：
文献类型：
--
作者：
M. Balde;U. Boscain;P. Mason
本文研究了平面线性切换系统的稳定性问题，其中实矩阵A1，A2∈ℝ2×2是Hurwitz矩阵，u(·)：[0，∞[→{0，1}是可测函数。给出了系统对任意切换函数u(·)渐近稳定的在A1和A2上坐标不变的充分必要条件。新条件统一了以往文献中给出的条件，简化为研究4例，而不是20例。大多数情况是从函数的角度分析的。
This article is concerned with the stability problem for the planar linear switched system , where the real matrices A 1, A 2 ∈ ℝ2×2 are Hurwitz and u(·) : [0, ∞ [→ {0, 1} is a measurable function. We give coordinate-invariant necessary and sufficient conditions on A 1 and A 2 under which the system is asymptotically stable for arbitrary switching functions u(·). The new conditions unify those given in previous papers and are simpler to be verified since we reduced to study 4 cases instead of 20. Most of the cases are analysed in terms of the function .