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Asymptotical stability of 2-D linear discrete stochastic systems

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Title: Asymptotical stability of 2-D linear discrete stochastic systems
Authors: Cui, Jia-Rui1 jiarui.cui@gmail.com, Li, Qing1, Hu, Guang-Da1, Zhu, Qiao1, Zhang, Xiao-Bing2
Source: Digital Signal Processing. Jul2012, Vol. 22 Issue 4, p628-632. 5p.
Subjects: Stochastic systems, Kronecker products, Stochastic matrices, Nonnegative matrices, White noise theory, Asymptotic theory of system theory
Abstract: Abstract: 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–Marchesiniʼs 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. [Copyright &y& Elsevier]
Copyright of Digital Signal Processing is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 74985733
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PubType: Periodical
PubTypeId: serialPeriodical
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  Data: <searchLink fieldCode="JN" term="%22Digital+Signal+Processing%22">Digital Signal Processing</searchLink>. Jul2012, Vol. 22 Issue 4, p628-632. 5p.
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  Data: <searchLink fieldCode="DE" term="%22Stochastic+systems%22">Stochastic systems</searchLink><br /><searchLink fieldCode="DE" term="%22Kronecker+products%22">Kronecker products</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+matrices%22">Stochastic matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Nonnegative+matrices%22">Nonnegative matrices</searchLink><br /><searchLink fieldCode="DE" term="%22White+noise+theory%22">White noise theory</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+theory+of+system+theory%22">Asymptotic theory of system theory</searchLink>
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  Data: Abstract: 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–Marchesiniʼs 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. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Digital Signal Processing is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.dsp.2012.03.005
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      – Code: eng
        Text: English
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        PageCount: 5
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        Type: general
      – SubjectFull: Kronecker products
        Type: general
      – SubjectFull: Stochastic matrices
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      – SubjectFull: Nonnegative matrices
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      – SubjectFull: White noise theory
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      – SubjectFull: Asymptotic theory of system theory
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              Text: Jul2012
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              Y: 2012
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