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SCIENCE CHINA Information Sciences, Volume 64 , Issue 5 : 152206(2021) https://doi.org/10.1007/s11432-020-2913-x

Finite-time asynchronous dissipative filtering of conic-type nonlinear Markov jump systems

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  • ReceivedMar 5, 2020
  • AcceptedApr 30, 2020
  • PublishedMar 25, 2021

Abstract


Acknowledgment

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61673001, 61722306), State Key Program of National Natural Science Foundation of China (Grant No. 61833007), Foundation for Distinguished Young Scholars of Anhui Province (Grant No. 1608085J05), Key Support Program of University Outstanding Youth Talent of Anhui Province (Grant No. gxydZD2017001), and Serbian Ministry of Education, Science and Technological Development (Grant No. 451-03-68/2020-14/200108).


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  • Figure 1

    (Color online) (a) The system mode; (b) the filter mode.

  • Table 1  

    Table 1Nomenclature table

    NotationDescription
    ${\boldsymbol~E}\{\cdot\}$The mathematical expectation operator
    $\epsilon_{\rm~max}(U)$ The maximum eigenvalue of $U$
    $\epsilon_{\rm~min}(U)$ The minimum eigenvalue of $U$
    $\mathbb{R}^{n}$textit n-dimensional Euclidean space
    $\mathbb{R}^{n\times~m}$ $n\times~m$ real matrix
    $\text{diag}\{A\;B\}$Block-diagonal matrix of $~A$ and $B$
    $I$Unit matrix
    $A^{-1}$Matrix inverse
    $A^\mathrm{T}$Matrix transpose
    $\ast$Symmetric matrix
    $\mathsf{Her}(A)$The sum of $A$ and transposition of $A$
  • Table 2  

    Table 2$\Phi$ values for three various cases

    Case I: synchronousCase II: partially asynchronousCase III: asynchronous
    $\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$ $\left[\begin{array}{cc}1&0\\0.25&0.75~\end{array}\right]$ $\left[\begin{array}{cc}0.9&0.1\\0.9&0.1 \end{array}\right]$
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