158
8 Filtering-Based Robust Fault Detection of Fuzzy Multi-model Jumping System
Figure 8.4 displays the residual evolution function f (r e f ) in fault case and nonfault case. With a selected threshold J th = sup ω(t)∈L 2 , f (t)=0 E{
15
0 r
T
e f (t) r e f (t)dt} =
1.72, we can obtained that f (r e f ) = E
8.6
0 r
T
e f (t)r e f (t)dt
= 0.92 > J th . Therefore, the occurred fault will be detected within 1.0 s after its appearance.
8.3 Conclusions
For nonlinear multi-model jumping system with time-delays and uncertainties, the
robust FDF design problem is studied. Based on the Lyapunov–Karasovsky functional method and LMIs techniques, sufficient conditions for the existence of fuzzy
robust FDF are given and proved, and the design problem is expressed as an optimization problem. An example is given to illustrate the contribution of the main
results.
8 Filtering-Based Robust Fault Detection of Fuzzy Multi-model Jumping System
Figure 8.4 displays the residual evolution function f (r e f ) in fault case and nonfault case. With a selected threshold J th = sup ω(t)∈L 2 , f (t)=0 E{
15
0 r
T
e f (t) r e f (t)dt} =
1.72, we can obtained that f (r e f ) = E
8.6
0 r
T
e f (t)r e f (t)dt
= 0.92 > J th . Therefore, the occurred fault will be detected within 1.0 s after its appearance.
8.3 Conclusions
For nonlinear multi-model jumping system with time-delays and uncertainties, the
robust FDF design problem is studied. Based on the Lyapunov–Karasovsky functional method and LMIs techniques, sufficient conditions for the existence of fuzzy
robust FDF are given and proved, and the design problem is expressed as an optimization problem. An example is given to illustrate the contribution of the main
results.