This paper deals with the problem of mixed H∞ and passivity performance analysis of digital filters subject to Markovian jumping parameters, external disturbances, time delays and bounds of the nonlinearity functions. By employing Lyapunov theory and matrix decomposition technique, a novel sufficient condition is established. The proposed criterion ensures that the underlying system is stochastically stable and satisfies a mixed H∞ and passivity performance index simultaneously. The obtained criterion can also be employed to solve the H∞ problem or the passivity problem in a unified framework. Moreover, the problem is formulated to obtain optimal mixed H∞ and passivity performance index of the interfered digital filters. The effectiveness and superiority of our proposed results are illustrated by three examples.

中文翻译：

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具有马尔可夫跳跃参数和延迟的干扰数字滤波器的混合 H∞ 和无源性能分析

本文主要针对混合问题H∞和受马尔可夫跳跃参数、外部干扰、时间延迟和非线性函数边界影响的数字滤波器的无源性能分析。利用李雅普诺夫理论和矩阵分解技术，建立了一个新的充分条件。所提出的标准确保了基础系统是随机稳定的并满足混合H∞和被动性能指标同时进行。得到的准则也可以用来解决H∞问题或被动问题在一个统一的框架中。此外，该问题被制定为获得最优混合H∞和受干扰数字滤波器的无源性能指标。我们提出的结果的有效性和优越性通过三个例子来说明。