Robust fault detection for continuous-time switched delay systems: an linear matrix inequality approach

Abstract

This paper deals with the problem of robust fault detection for discrete-time switched systems with state delays under arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs and model uncertainties, the estimation error between the residuals and the faults is minimized. The problem of robust fault detection is converted into an H∞ filtering problem. By switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed method.

A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches

“…Alternatively, the multi-object optimization problem described by (4) can be reformulated by linear matrix inequality (LMI), which has been a popular method for fault diagnosis research and applications owing to its wide applicability to a variety of dynamic systems. Recent development of the LMI-based fault diagnosis can be found for various systems such as Lipschitz nonlinear systems [48], TS fuzzy nonlinear systems [49,50], time-delay systems [51], switching systems [52], and application to structure damage detection [53], and shaft crack detection [54] etc.…”

Fault Detection for a Class of Impulsive Switched Systems

“…In practical applications, the frequency characteristics of faults is in a limited ranger. Then similar to [20,21], the stable weighted matrix W f (s) is introduced to improve the system performance and emphasize the captured frequency characteristics of faults.…”

“…Compared with the stability and the stabilization problems [18] , the FD design problem in switched systems is still in the early stage of development [19,20] , let alone the impulsive switched systems. Moreover, since the existing approaches about FD problem or switched systems are not appropriate for FD problem for nonlinear impulsive switched systems, the new technique should solve the impulsive case.…”

Mixed l −/l 1 fault detection observer design for positive switched systems with time-varying delay via delta operator approach

“…This means that the fault detection and isolation systems have to be sensitive to faults and simultaneously robust to the noise and disturbances. Several approaches using the H ∞ norm techniques have been largely developed for the design of robust fault detection observers or filters [22][23][24], where the H ∞ norm has been widely accepted as a good measure of robustness against unknown noise and disturbances. However, it should be pointed out that H ∞ norm does not consist with the main objective of fault detection, i.e., sensitivity to faults, because it measures the maximum effect of an input on an output.…”