SCIENCE CHINA Information Sciences, Volume 64 , Issue 10 : 200201(2021) https://doi.org/10.1007/s11432-021-3280-4

Fault estimation and fault-tolerant control for linear discrete time-varying stochastic systems

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  • ReceivedFeb 15, 2021
  • AcceptedMay 8, 2021
  • PublishedSep 14, 2021



This work was supported by National Natural Science Foundation of China (Grant Nos. 62073144, 61733008, 61873099, 61803108), National Science Foundation of Guangdong Province (Grant No. 2020A1515010441), and Guangzhou Science and Technology Planning Project (Grant Nos. 202002030158, 202002030389), Key-area Research and Development Program of Guangdong Province (Grant No. 2020B0909020001), Science and Technology Research Project of Chongqing Education Commission (Grant Nos. KJZD-M201900801, KJQN201900831), and Chongqing Natural Science Foundation (Grant No. cstc2020jcyj-msxmX0077).


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  • Figure 1

    The diagram of the proposed fault-tolerant scheme.

  • Figure 4

    (Color online) The mean square values $E\|e_{x_k}\|^2$ and $E\|e_{f_k}\|^2$.

  • Figure 7

    (Color online) The state $x_k$ of system (1) under $\bar{f}_k$.


    Algorithm 1 A cone complementarity linearization algorithm

    Find a set of feasible solutions of LMI (2019filter1-ewdd)denoted by $\{P_{k,0}\}_{k\in~{\mathcal~N}_{T-1}}$,$\{X_{k,0}\}_{k\in~{\mathcal~N}_{T-1}}$;if there is none, the procedure exits. Set $i=0$.

    Solve the convex optimization problem to obtain $P_{k,i+1}$ and$X_{k,i+1}$: $$ \min_{X_{k,i+1},P_{k,i+1}} \sum_{k=0}^{T-1}\{\text{trace}({P}_{k,i}X_{k,i+1})+\text{trace}({X}_{k,i}P_{k,i+1})\} $$ subject to LMIs $$ \left[\begin{array}{ccc} -P_{k,i+1}&\bar{A}_k'&\bar{C}_k'\\ \bar{A}_k&-X_{k+1,i+1}&0\\ \bar{C}_k &0&-X_{k+1,i+1} \end{array}\right]<0, k\in {\mathcal N}_{T-1}, $$ and $$ \left[\begin{array}{cc} P_{k,i+1} & I \\ I & X_{k,i+1} \end{array}\right]\geq0, k\in {\mathcal N}_{T-1}. $$

    If a stopping criterion$|\sum_{k=0}^{T-1}\{\text{trace} ({P}_{k,i}X_{k,i+1})+\text{trace}({X}_{k,i}P_{k,i+1})\}-4nT|<\epsilon$ for a prescribed $\epsilon>0$ is satisfied,the procedure stops. Otherwise, set $i=i+1$and go back to step 2.


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