This paper is devoted to the problem of $$ H_{\infty } $$ H ∞ filtering for a class of discrete-time singular Markovian jump systems with generally uncertain transition rates. Each transition rate of the jumping process is completely unknown or only the estimated value is known. The objective is to design a $$ H_{\infty } $$ H ∞ filter such that the resulting filtering error system is stochastically admissible (regular, causal and stochastically stable) while satisfying a prescribed $$ H_{\infty } $$ H ∞ performance $$ \gamma $$ γ . Sufficient conditions are derived that can guarantee the filtering error system is $$ H_{\infty } $$ H ∞ stochastically admissible. Moreover, explicit expression of the filter gains is obtained by solving a set of strict linear matrix inequalities. Finally, a numerical example is included to illustrate the effectiveness of the proposed method.

中文翻译：

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$$ H_{\infty } $$ 对具有一般不确定转换率的离散时间奇异马尔可夫跳跃系统进行过滤

本文致力于研究一类过渡率一般不确定的离散时间奇异马尔可夫跳跃系统的$$H_{\infty}$$H ∞ 滤波问题。跳跃过程的每个跃迁率完全未知或只有估计值已知。目标是设计一个 $$ H_{\infty } $$ H ∞ 过滤器，使得产生的过滤误差系统在满足规定的 $$ H_{\infty } $$ H 的同时是随机可接受的（正则、因果和随机稳定的） ∞ 性能 $$ \gamma $$ γ 。推导出了充分的条件，可以保证过滤误差系统是$$ H_{\infty } $$ H ∞ 随机允许的。此外，滤波器增益的显式表达是通过求解一组严格的线性矩阵不等式来获得的。最后，