Almost sure asymptotic stabilizability for deterministic systems with wiener processes
Almost sure asymptotic stabilizability for deterministic systems with wiener processes
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DOI：
10.1109/med.2012.6265672
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
Y. Nishimura;K. Tanaka;Y. Wakasa
中科院分区：
文献类型：
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作者：
Y. Nishimura;K. Tanaka;Y. Wakasa
本文讨论了通过添加一维标准Wiener过程随机化的确定性系统的几乎处处渐近稳定性。首先，我们澄清了确定性李雅普诺夫稳定性理论和Hasminskii提出的随机稳定性理论之间的差异，并表明概率的局部渐近稳定性在随机化问题中会带来麻烦。其次，我们描述了李雅普诺夫稳定性理论的基础上几乎必然的稳定性，提出了由巴尔迪和Cesaroni，并表明稳定性是“几乎相同”的确定性李雅普诺夫稳定性。第三，我们调查随机化问题简要，并表明，Stratonovich积分是有效的，这样的问题的基础上一维维纳过程。最后，我们通过线性随机系统的数值模拟，得到了随机李雅普诺夫函数保证几乎必然稳定性的必要条件，并讨论了Hasminskii稳定性与巴尔迪和Cesaroni稳定性之间的差异。
In this paper, we discuss almost sure asymptotic stability for deterministic systems, which are randomized by adding one-dimensional standard Wiener processes. First, we clarify the difference between the deterministic Lyapunov stability theory and the stochastic stability theory proposed by Hasminskii, and show that local asymptotic stability in probability causes trouble in randomization problems. Second, we describe the Lyapunov stability theory based on almost sure stability, as proposed by Bardi and Cesaroni, and show that the stability is “almost the same” as the deterministic Lyapunov stability. Third, we survey randomization problems briefly, and show that Stratonovich integrals are valid for such problems based on one-dimensional Wiener processes. Finally, we derive the necessary conditions for stochastic Lyapunov functions to ensure almost sure stabilities and discuss the difference between Hasminskii's stabilities and those of Bardi and Cesaroni via linear stochastic systems with numerical simulations.