66
4 Finite-Frequency Robust Filtering for Multi-model Jumping System
4.3 Numeral Examples
Example 4.1 Consider the continuous-time multi-model jumping system (4.1) with
parameters given by:
Mode 1:
A 1 =
−1 −0.4
0.5 −0.81
, B d1 =
1
1
, C 11 =
−0.5 −0.4
,
C 21 =
−0.1 0.2
, D d1 =
0.2
;
Mode 2:
A 2 =
−1.4 −0.26
0.9 −0.13
, B d2 =
0.2
0.26
, C 12 =
0.1 0.3
,
C 22 =
0.1 0.1
, D d2 =
0.3
;
Mode 3:
A 3 =
0.2 −1.1
0.1 −0.4
, B d3 =
0.5
−0.3
, C 13 =
0.4 0.3
,
C 23 =
0.1 −0.3
, D d3 =
0.1
.
And the transition rate matrix is defined as:
=
⎡
⎣
−0.8 0.3 0.5
0.4 −0.6 0.2
0.6 0.3 −0.9
⎤
⎦ .
Suppose γ = 0.1, 1 = 20, and 2 = 90. The filter parameters for three methods are
obtained by solving LMIs (4.14)–(4.15):
A F1 =
−2.4454 1.680
0.8605 −2.7079
, B F1 =
1.5621
−1.0026
,
C F1 = [−0.07170.0889],
D F1 = −0.2046,
A F2 =
−2.5717 −0.0470
−0.0013 −0.9356
, B F3 =
−0.4035
−0.7679
,
C F2 = [0.06640.0368],
D F2 = −0.3026,
4 Finite-Frequency Robust Filtering for Multi-model Jumping System
4.3 Numeral Examples
Example 4.1 Consider the continuous-time multi-model jumping system (4.1) with
parameters given by:
Mode 1:
A 1 =
−1 −0.4
0.5 −0.81
, B d1 =
1
1
, C 11 =
−0.5 −0.4
,
C 21 =
−0.1 0.2
, D d1 =
0.2
;
Mode 2:
A 2 =
−1.4 −0.26
0.9 −0.13
, B d2 =
0.2
0.26
, C 12 =
0.1 0.3
,
C 22 =
0.1 0.1
, D d2 =
0.3
;
Mode 3:
A 3 =
0.2 −1.1
0.1 −0.4
, B d3 =
0.5
−0.3
, C 13 =
0.4 0.3
,
C 23 =
0.1 −0.3
, D d3 =
0.1
.
And the transition rate matrix is defined as:
=
⎡
⎣
−0.8 0.3 0.5
0.4 −0.6 0.2
0.6 0.3 −0.9
⎤
⎦ .
Suppose γ = 0.1, 1 = 20, and 2 = 90. The filter parameters for three methods are
obtained by solving LMIs (4.14)–(4.15):
A F1 =
−2.4454 1.680
0.8605 −2.7079
, B F1 =
1.5621
−1.0026
,
C F1 = [−0.07170.0889],
D F1 = −0.2046,
A F2 =
−2.5717 −0.0470
−0.0013 −0.9356
, B F3 =
−0.4035
−0.7679
,
C F2 = [0.06640.0368],
D F2 = −0.3026,