Abstract This paper addresses the problem of the extended dissipative filtering for a class of Markovian jump interval-valued fuzzy systems with uncertain transition rates. First, a sufficient condition of stochastic asymptotic stability and extended dissipativity is provided. Then, by introducing some additional matrices, the matrices in this sufficient condition can be decomposed into a form with only one part and its transpose containing the unknown parametric matrices of filter, which is vitally important for establishing a new sufficient condition and designing an extended dissipative filter via the Projection Lemma. Attention is focused on the applications of this Projection Lemma twice by virtue of the feature of extended dissipative performance which differs from existing work and produces better estimated effects. The new sufficient condition is of nonlinear form with respect to some matrix variables, which makes the determination of extended dissipative filter difficult. Fortunately, by transforming nonlinear matrix inequalities into a quadratic optimization problem with linear matrix inequality constraints, the extended dissipative filter is developed by virtue of a cone complementarity linearization algorithm. Finally, two numerical examples are given to show the effectiveness of our proposed approach.

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具有不确定转移率的马尔可夫跳跃区间值模糊系统的扩展耗散滤波

摘要 本文解决了一类转换率不确定的马尔可夫跳跃区间值模糊系统的扩展耗散滤波问题。首先，提供了随机渐近稳定性和扩展耗散性的充分条件。然后，通过引入一些额外的矩阵，这个充分条件下的矩阵可以分解成只有一部分的形式，其转置包含滤波器的未知参数矩阵，这对于建立新的充分条件和设计扩展耗散矩阵至关重要。通过投影引理过滤。由于与现有工作不同并产生更好的估计效果的扩展耗散性能特征，因此两次关注该投影引理的应用。新的充分条件对于一些矩阵变量是非线性形式的，这使得扩展耗散滤波器的确定变得困难。幸运的是，通过将非线性矩阵不等式转化为具有线性矩阵不等式约束的二次优化问题，扩展耗散滤波器是通过锥互补线性化算法开发的。最后，给出了两个数值例子来证明我们提出的方法的有效性。扩展耗散滤波器是通过锥互补线性化算法开发的。最后，给出了两个数值例子来证明我们提出的方法的有效性。扩展耗散滤波器是通过锥互补线性化算法开发的。最后，给出了两个数值例子来证明我们提出的方法的有效性。