Asymptotical stability of 2-D linear discrete stochastic systems

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• 作者：Jia-Rui Cui^a ; ^{jiarui.cui@gmail.com}  ; [Author Vitae] ; Qing Li^a  ; [Author Vitae] ; Guang-Da Hu^a  ; [Author Vitae] ; Qiao Zhu^a  ; [Author Vitae] ; Xiao-Bing Zhang^b  ; [Author Vitae]
• 关键词：Two-dimensional discrete stochastic systems ; Mean-square stability ; Kronecker product ; Nonnegative matrix ; White noise
• 刊名：Digital Signal Processing
• 出版年：2012
• 期刊代码：128_10512004
• 类别：cp
• 出版时间：July, 2012
• 卷：22
• 期：4
• 页码：628-632
• 文件大小：200 K

摘要

The main goal of the present paper is to find computable stability criteria for two-dimensional stochastic systems based on Kronecker product and nonnegative matrices theory. First, 2-D discrete stochastic system model is established by extending system matrices of the well-known Fornasini-Marchesini始s second model into stochastic matrices. The elements of these stochastic matrices are second-order, weakly stationary white-noise sequences. Second, a necessary and sufficient condition for 2-D stochastic systems is presented, this is the first time that has been proposed. Third, computable mean-square asymptotic stability criteria are derived via Kronecker product and the nonnegative matrix theory. The criteria are only sufficient conditions. Finally, illustrative examples are provided.