Global Stability of Feedback Systems with Multiplicative Noise on the Nonnegative Orthant
Global Stability of Feedback Systems with Multiplicative Noise on the Nonnegative Orthant
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DOI：
10.1137/16m1101076
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发表时间：
2018-06
期刊：
影响因子：
--
通讯作者：
Jifa Jiang;Xiang Lv
中科院分区：
文献类型：
--
作者：
Jifa Jiang;Xiang Lv
We investigate the dynamical behavior of pull-back trajectories for feedback systems with multiplicative noise and prove that there exists a globally stable positive random equilibrium in the nonnegative orthant $\Bbb{R}^d_+$, where the global stability means that all pull-back trajectories originating from nonnegative orthant converge to this positive random equilibrium almost surely. The output functions (feedback functions) are assumed to either possess bounded derivatives or be uniformly bounded away from zero. In the first case, we first prove the joint measurability of the metric dynamical system $\theta$ with respect to the $\sigma$-algebra $\mathscr{B}(\Bbb{R_-})\otimes\mathscr{F}_-$, where $\mathscr{F}_-=\sigma\{\omega\mapsto W_t(\omega):t\leq0\}$ is the past $\sigma$-algebra and $W_t(\omega)$ is an $\Bbb{R}^d$-valued two-sided Wiener process, and then combine the $\mathcal{L}^1$-integrability of the tempered random variable coming from the definition of the top Lyapunov exponent and the independ...
