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Minimum System Sensitivity Study of Linear Discrete Time Systems for Fault Detection

机译：故障检测线性离散时间系统的最小系统灵敏度研究

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摘要

Fault detection is a critical step in the fault diagnosis of modern complex systems. An important notion in fault detection is the smallest gain of system sensitivity, denoted as (H)_ index, which measures the worst fault sensitivity. This paper is concerned with characterizing (H)_ index for linear discrete time systems. First, a necessary and sufficient condition on the lower bound of (H)_ index in finite time horizon for linear discrete time-varying systems is developed. It is characterized in terms of the existence of solution to a backward difference Riccati equation with an inequality constraint. The result is further extended to systems with unknown initial condition based on a modified (H)_ index. In addition, for linear time-invariant systems in infinite time horizon, based on the definition of the (H)_ index in frequency domain, a condition in terms of algebraic Riccati equation is developed. In comparison with the well-known bounded real lemma, it is found that (H)_ index is not completely dual to (H)_∞ norm. Finally, several numerical examples are given to illustrate the main results.
机译：故障检测是现代复杂系统故障诊断中的关键步骤。故障检测中的一个重要概念是系统灵敏度的最小增益，表示为（H）_ index，它衡量最差的故障灵敏度。本文涉及表征线性离散时间系统的（H）_指标。首先，建立了线性离散时变系统在有限时间范围内（H）_指标下界的充要条件。它的特征是存在不等式约束的向后差分Riccati方程的解。基于修改后的（H）_索引，结果可进一步扩展到初始条件未知的系统。此外，对于无限时域内的线性时不变系统，基于频域（H）_指标的定义，建立了代数Riccati方程的条件。与众所周知的有界实引理相比，发现（H）_指标不是（H）_∞范数的完全对偶。最后，给出了几个数值示例来说明主要结果。

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  • 来源
    《Mathematical Problems in Engineering》 |2013年第1期|276987.1-276987.13|共13页
  • 作者

    Xiaobo Li; Hugh H. T. Liu;

  • 作者单位

    Institute for Aerospace Studies, University of Toronto, Toronto, ON, Canada M3H 5T6;

    Institute for Aerospace Studies, University of Toronto, Toronto, ON, Canada M3H 5T6;

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