Robust Estimation Design for Unknown Inputs Fuzzy Bilinear Models: Application to Faults Diagnosis - Complex System Modelling and Control Through Intelligent Soft Computations - page 667

1.5

x1 real

x1 estimate

1

0.5

0

0 1 2 3 4 5 6 7

8 9 10

t(s)

Fig. 9 Evolution of the predator population x 1 and its estimate with unmeasurable decision
variables

2.5

2

x2 real
x2 estimate

1.5

1

0.5

0

0 1 2 3 4 5 6 7 8 9 10

t(s)

Fig. 10 Evolution of the predator population x 2 and its estimate with unmeasurable decision
variables

5.3 Fault Detection

In this subsection, we will consider the same system of predator-prey model subject
to fault:

8
<

x 1 ð _ t Þ ¼ ax 1 ð t Þ bx 1 ð t Þ x 2 ð t Þþ 0 : 1d ð t Þþ 0 : 5f ð t Þ

x 2 ð _ t Þ ¼ cx 1 ð t Þ x 2 ð t Þ dx 2 ð t Þ fx 2 ð t Þ u ð t Þþ 0 : 3d ð t Þ ð 112 Þ

:

y ¼ 0 : 4x 1 ð t Þþ x 2 ð t Þ