This article deals with the problem of fault detection observer design for continuous-time periodic piecewise linear systems. Mixed performance index is introduced, which results in a trade-off between robustness to unknown input and sensitivity to a fault. Based on a class of Lyapunov functions with time-varying Lyapunov matrices, sufficient conditions are developed to investigate the existence of periodic piecewise fault detection observer with weighted performance. A tractable iterative algorithm is proposed to establish the desired periodic piecewise fault detection observer. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

中文翻译：

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周期性分段线性系统的故障检测观测器设计

本文处理连续时间周期分段线性系统的故障检测观测器设计问题。引入了混合性能指标，这导致了对未知输入的鲁棒性和对故障的敏感性之间的权衡。基于一类具有时变李雅普诺夫矩阵的李雅普诺夫函数，开发了充分条件来研究具有加权性能的周期性分段故障检测观测器的存在。提出了一种易于处理的迭代算法来建立期望的周期性分段故障检测观测器。最后，提供了一个数值例子来说明所提出方法的有效性。