Stability of planar switched systems: the linear single, input case
Stability of planar switched systems: the linear single, input case
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DOI：
10.1109/cdc.2002.1184385
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发表时间：
2002-12
期刊：
影响因子：
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通讯作者：
U. Boscain
中科院分区：
文献类型：
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作者：
U. Boscain
本文研究了动力系统x/spl dot/（t）=u（t）Ax（t）+（1-u（t））Bx（t）的原点的稳定性，其中A和B是两个2/spl × 2真实的矩阵，其特征值具有严格负的真实的部分，x/spl在/R/sup 2/和u（.）中：[0，/spl infin/[/spl rint/ [0，1]是完全随机可测函数。更准确地说，我们找到了一个（坐标不变）的必要和充分条件A和B的原点是渐近稳定的每个功能u（。）。这个二维问题假定特别感兴趣，因为更高维度的线性系统可以减少到我们的情况。两个未发表的例子（更困难）的情况下，两个矩阵都有真实的特征值进行了详细分析。
We study the stability of the origin for the dynamical system, x/spl dot/(t)=u(t)Ax(t)+(1-u(t))Bx(t), where A and B are two 2/spl times/2 real matrices with eigenvalues having strictly negative real part, x/spl isin/R/sup 2/ and u(.):[0, /spl infin/[/spl rarr/ [0, 1] is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). This bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation. Two unpublished examples in the (more difficult) case in which both matrices have real eigenvalues are analyzed in details.