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

作者：Li Xiaobo; Liu Hugh H T^*

来源：Mathematical Problems in Engineering, 2013, 2013: 276987.

DOI：10.1155/2013/276987

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-infinity norm. Finally, several numerical examples are given to illustrate the main results.

• 出版日期2013