Mean-Square Stabilizability Under Unstructured Stochastic Multiplicative Uncertainties: A Mean-Square Small-Gain Perspective

Jianqi Chen, T. Qi, Yanling Ding, Hui Peng, Jing Chen, S. Hara
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Abstract

In this paper we study the stability and stabilizability problems of multi-input, multi-output linear time-invariant systems subject to stochastic multiplicative uncertainties under the mean-square criterion. We consider the matrix-valued unstructured perturbations, which consist of static, zero-mean stochastic processes. We first obtain a necessary and sufficient condition to ensure the stability of the open-loop stable system against uncertainties in the mean-square sense. Based on the obtained mean-square stability condition, we further answer the question: How can an open-loop unstable system be stabilized by output feedback in the mean-square sense despite the presence of such stochastic uncertainties? The complete and explicit stabilizability conditions are derived, which reveal how the locations and directions associated with unstable poles and nonminimum phase zeros of the plant coupled together affect the mean-square stabilizability.
非结构随机乘法不确定性下的均方稳定性:均方小增益视角
在均方准则下,研究了具有随机乘法不确定性的多输入多输出线性定常系统的稳定性和可稳定性问题。我们考虑由静态、零均值随机过程组成的矩阵值非结构化扰动。首先得到了开环稳定系统对均方不确定性稳定的一个充分必要条件。基于得到的均方稳定性条件,我们进一步回答了这样一个问题:在存在这些随机不确定性的情况下,开环不稳定系统如何通过均方意义上的输出反馈来稳定?导出了完整的、显式的稳定性条件,揭示了不稳定极点和非最小相零耦合的位置和方向对均方稳定性的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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