A note on simple randomly switched linear systems
A note on simple randomly switched linear systems
复制标题
关于简单随机切换线性系统的注记
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
G. Lagasquie
中科院分区：
文献类型：
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作者：
G. Lagasquie
我们构建了一个平面的过程，从两个Hurwitz矩阵（所有的特征值有负的真实的部分）建立的两个线性系统的流量之间随机切换。这里的目标是根据切换速率来研究长时间行为。我们将看到，即使两个系统是稳定的，如果我们明智地选择切换速率，也有可能获得爆破。最后，我们将看到不变测度的尾部（当切换时间遵循指数规律时）与使过程爆炸的确定性控制的存在之间的联系。
We construct a planar process that switches randomly between the flows of two linear systems built from two Hurwitz matrices (all eigenvalues have negative real parts). The goal here is to study the long time behaviour according to the switching rates. We will see that, even if the two systems are stable, it is possible to obtain a blow up if we choose the switching rates wisely. Finally we will see a connection, between the tail of the invariant measure (when the switching times follow an exponential law) and the existence of a deterministic control that makes the process explode.