A Lyapunov approach to iISS and iNSS for stochastic systems in path-wise probability
A Lyapunov approach to iISS and iNSS for stochastic systems in path-wise probability
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DOI：
10.1109/acc.2015.7172279
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发表时间：
2015-07
期刊：
影响因子：
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通讯作者：
H. Ito;Y. Nishimura
中科院分区：
文献类型：
--
作者：
H. Ito;Y. Nishimura
对于随机非线性动力系统，本文给出了几个路径意义下的稳定性概念。发展了Lyapunov刻画来验证这些性质。这里研究的概念比一般的输入-状态稳定性和噪声-状态稳定性所保证的有界性性质更严格，它们的概率是在每个时刻获取的。证明了文献中频繁构造的Lyapunov函数不仅建立了瞬时概率性质，而且建立了路径概率性质。当人们想要估计初始效果的收敛时，就会出现差异。如果扩散场与Lyapunov函数的梯度远距离正交，这种差异就消失了。
For stochastic nonlinear dynamical systems, this paper addresses several stability notions in the path-wise sense. Lyapunov characterizations are developed to verify those properties. The notions investigated here are stricter than boundedness properties ensured by popular input-to-state stability and noise-to-state stability whose probability is taken at each instant. It is demonstrated that Lyapunov functions constructed frequently in the literature not only establish the instantaneous probabilistic properties, but also path-wise probabilistic ones. Differences appear when one wants to estimate the convergence of initial effect. The differences disappear if diffusion fields are remotely orthogonal to the gradient of Lyapunov functions.