This paper concerns the mode dependent H filter design for continuous Markov jump linear systems. The filter gain to be designed is assumed to have additive variations and the transition probabilities are allowed to be known, uncertain with known bounds and unknown. Attention is focused on the design of a mode dependent nonfragile full order filter, which guarantees the filtering error system to be stochastically stable and has a prescribed H disturbance attenuation performance. Sufficient conditions for the desired filter design are given in the framework of linear matrix inequality. If the filter gain variations become zero and the transition probabilities are completely known, the proposed method is reduced to the standard H filtering results. A numerical examples is given to show the effectiveness of the proposed method.

References

References
1.
Boukas
,
E. K.
,
2005
,
Stochastic Switching Systems: Analysis and Design
,
Birkhauser
,
Berlin
.
2.
Costa
,
O. L. V.
,
Fragoso
,
M. D.
, and
Marques
,
R. P.
,
2005
,
Discrete-Time Markov Jump Linear Systems
,
Springer-Verlag
,
London
.
3.
Mariton
,
M.
,
1990
,
Jump Linear Systems in Automatic Control
,
Marcel Dekker
,
New York
.
4.
Feng
,
X.
,
Loparo
,
K. A.
,
Ji
,
Y.
, and
Chizeck
,
H. J.
,
1992
, “
Stochastic Stability Properties of Jump Linear Systems
,”
IEEE Trans. Autom. Control
,
37
(
1
), pp.
38
53
.10.1109/9.109637
5.
Boukas
,
E. K.
,
2009
, “
H∞ Control of Discrete-Time Markov Jump Systems With Bounded Transition Probabilities
,”
Opt. Control Appl. Methods
,
30
(
5
), pp.
477
494
.10.1002/oca.870
6.
Zhang
,
L.
, and
Lam
,
J.
,
2010
, “
Necessary and Sufficient Conditions for Analysis and Synthesis of Markov Jump Linear Systems With Incomplete Transition Descriptions
,”
IEEE Trans. Autom. Control
,
53
(
10
), pp.
1695
1701
.10.1109/TAC.2010.2046607
7.
Liu
,
H.
,
Ho
,
D.W.C.
, and
Sun
,
F.
,
2008
, “
Design of H∞ Filter for Markov Jumping Linear Systems With Non-Accessible Mode Information
,”
Automatica
,
44
(
10
), pp.
2655
2660
.10.1016/j.automatica.2008.03.011
8.
Ji
,
Y.
, and
Chizeck
,
H.
,
1990
, “
Controllability, Stabilizability, and Continuous Time Markovian Jump Linear Quadratic Control
,”
IEEE Trans. Autom. Control
,
35
(
7
), pp.
777
788
.10.1109/9.57016
9.
Costa
,
O. L. V.
, and
Guerra
,
S.
,
2002
, “
Robust Linear Filtering for Discrete-Time Hybrid Markov Linear Systems
,”
Int. J. Control
,
75
(
10
), pp.
712
727
.10.1080/00207170210139502
10.
Xiong
,
J.
, and
Lam
,
J.
,
2006
, “
Fixed-Order Robust H∞ Filter Design for Markovian Jump Systems With Uncertain Switching Probabilities
,”
IEEE Trans. Signal Process.
,
54
(
4
), pp.
1421
1430
.10.1109/TSP.2006.871880
11.
Zhang
,
H.
,
Shi
,
Y.
, and
Mehr
,
A. S.
,
2011
, “
Robust Weighted H∞ Filtering for Networked Systems With Intermittent Measurements of Multiple Sensors
,”
Int. J. Adapt. Control Signal Process
,
25
(
4
), pp.
313
330
.10.1002/acs.1200
12.
Zhang
,
H.
,
Shi
,
Y.
, and
Mehr
,
A. S.
,
2010
, “
Robust Energy-to-Peak Filtering for Networked Systems With Time-Varying Delays and Randomly Missing Data
,”
IET Control Theory & Applications
,
4
(12)
, pp.
2921
2936
.10.1049/iet-cta.2009.0243
13.
Ding
,
D.
, and
Yang
,
G.
,
2010
, “
Fuzzy Filter Design for Nonlinear Systems in Finite-Frequency Domain
,”
IEEE Trans. Fuzzy Syst.
,
18
(
5
), pp.
935
945
.10.1109/TFUZZ.2010.2058807
14.
Zhang
,
H.
,
Shi
,
Y.
,
Mehr
,
A. S.
, and
Huang
,
H.
,
2011
, “
Robust Energy-to-Peak FIR Equalization for Time-Varying Communication Channels With Intermittent Observations
,”
Signal Process.
,
91
(
7
), pp.
1651
1658
.10.1016/j.sigpro.2011.01.011
15.
Zhang
,
H.
,
Shi
,
Y.
, and
Mehr
,
A. S.
,
2012
, “
On H∞ Filtering for Discrete-Time Takagi-Sugeno Fuzzy Systems
,”
IEEE Trans. Fuzzy Syst.
,
20
(
2
), pp.
396
401
.10.1109/TFUZZ.2011.2175933
16.
Wang
,
G.
,
Zhang
,
Q.
, and
Sreeram
,
V.
,
2009
, “
Design of Reduced-Order H∞ Filtering for Markovian Jump Systems With Mode-Dependent Time Delays
,”
Signal Process.
,
89
(
2
), pp.
187
196
.10.1016/j.sigpro.2008.08.004
17.
Wang
,
G.
,
Zhang
,
Q.
, and
Sreeram
,
V.
,
2010
, “
Partially Mode-Dependent H∞ Filtering for Discrete-Time Markovian Jump Systems With Partly Unknown Transition Probabilities
,”
Signal Process.
,
90
(
2
), pp.
548
556
.10.1016/j.sigpro.2009.07.020
18.
Han
,
C.
, and
Zhang
,
H.
,
2009
, “
Linear Optimal Filtering for Discrete-Time Systems With Random Jump Delays
,”
Signal Process.
,
89
(
6
), pp.
1121
1128
.10.1016/j.sigpro.2008.12.016
19.
Zhang
,
H.
,
Mehr
,
A. S.
, and
Shi
,
Y.
,
2010
, “
Improved Robust Energy-to-Peak Filtering for Uncertain Linear Systems
,”
Signal Process.
,
90
(
9
), pp.
2667
2675
.10.1016/j.sigpro.2010.03.011
20.
De Souza
,
C. E.
, and
Fragoso
,
M. D.
,
2002
, “
H∞ Filtering for Markovian Jump Linear Systems
,”
Int. J. Syst. Sci.
,
33
(
11
), pp.
909
915
.10.1080/0020772021000017281
21.
Li
,
H.
, and
Fu
,
M.
,
1997
, “
A Linear Matrix Inequality Approach to Robust H∞ Filtering
,”
IEEE Trans. Signal Process.
,
45
(
9
), pp.
2338
2350
.10.1109/78.564176
22.
Shi
,
P.
,
Boukas
,
E. K.
, and
Agarwal
,
R. K.
,
1999
, “
Kalman Filtering for Continuous-Time Uncertain Systems With Markovian Jumping Parameters
,”
IEEE Trans. Autom. Control
,
44
(
8
), pp.
1592
1597
.10.1109/9.780431
23.
Yaz
,
E. E.
, and
Yaz
,
Y. I.
,
2000
, “
Reduced-Order Filtering of Jump Markov Systems With Noise-Free Measurements
,”
J. Franklin Inst.
,
337
(
7
), pp.
923
928
.10.1016/S0016-0032(00)00054-5
24.
Wang
,
Z.
,
Lam
,
J.
, and
Liu
,
X.
,
2003
, “
Nonlinear Filtering for State Delayed Systems With Markovian Switching
,”
IEEE Trans. Signal Process.
,
51
(
9
), pp.
2321
2328
.10.1109/TSP.2003.815373
25.
Wang
,
Z.
,
Lam
,
J.
, and
Liu
,
X.
,
2004
, “
Exponential Filtering for Uncertain Markovian Jump Time-Delay Systems With Nonlinear Disturbances
,”
IEEE Trans. Circuits Syst., II: Express Briefs
,
51
(
5
), pp.
262
268
.10.1109/TCSII.2004.825596
26.
Fang
,
Y.
, and
Loparo
,
K. A.
,
2002
, “
Stabilization of Continuous-Time Jump Linear Systems
,”
IEEE Trans. Autom. Control
,
47
(
10
), pp.
1590
1603
.10.1109/TAC.2002.803528
27.
Sworder
,
D. D.
,
1969
, “
Feedback Control for a Class of Linear Systems With Jump Parameters
,”
IEEE Trans. Autom. Control
,
14
(
1
), pp.
9
14
.10.1109/TAC.1969.1099088
28.
Costa
,
O. L. V.
,
1994
,
“Linear Minimum Mean Squares Error Estimation for Discrete-Time Markovian Jump Linear Systems
,”
IEEE Trans. Autom. Control
,
39
(
8
), pp.
1685
1689
.10.1109/9.310052
29.
Blom
,
H. A. P.
, and
Bar-Shalom
,
Y.
,
1988
, “
The Interacting Multiple Model Algorithm for Systems With Markovian Switching Coefficients
,”
IEEE Trans. Autom. Control
,
33
(
8
), pp.
780
783
.10.1109/9.1299
30.
de
Souza
,
C. E.
, and
Fragoso
,
M. D.
,
2002
, “
Robust H∞ Filtering for Uncertain Markovian Jump Linear Systems
,”
Int. J. Robust Nonlinear Control
,
12
(
5
), pp.
435
446
.10.1002/rnc.631
31.
Xu
,
S.
,
Chen
,
T.
, and
Lam
,
J.
,
2003
, “
Robust H∞ Filtering for Uncertain Markovian Jump Systems With Mode-Dependent Time Delays
,”
IEEE Trans. Autom. Control
,
48
(
5
), pp.
900
907
.10.1109/TAC.2003.820138
32.
de Souza
,
C. E.
,
Trofino
,
A.
, and
Barbosa
,
K. A.
,
2006
, “
Mode-Independent H∞ Filters for Markovian Jump Linear Systems
,”
IEEE Trans. Autom. Control
,
51
(
11
), pp.
1837
1841
.10.1109/TAC.2006.883060
33.
Chang
,
X.
, and
Yang
,
G.
,
2011
, “
Nonfragile H∞ Filtering of Continuous-Time Fuzzy Systems
,”
IEEE Trans. Signal Process.
,
59
(
4
), pp.
1528
1538
.10.1109/TSP.2010.2103068
34.
Keel
,
L. H.
, and
Bhattacharyya
,
S. P.
,
1997
, “
Robust, Fragile, or Optimal?,
IEEE Trans. Autom. Control
,
42
(
8
), pp.
1098
1105
.10.1109/9.618239
35.
Yang
,
G.
, and
Che
,
W.
,
2008
, “
Non-Fragile H∞ Filter Design for Linear Continuous-Time Systems
,”
Automatica
,
44
(
11
), pp.
2849
2856
.10.1016/j.automatica.2008.03.018
36.
Ding
,
D.
,
Li
,
X.
,
Yin
,
Y.
, and
Sun
,
C.
,
2012
, “
Nonfragile H∞ and H2 Filter Designs for Continuous-Time Linear Systems Based on Randomized Algorithms
,”
IEEE Trans. Ind. Electron. Control Instrum.
,
59
(
11
), pp.
4433
4442
.10.1109/TIE.2011.2159350
37.
Kang
,
Y.
,
Zhang
,
J.
, and
Ge
,
S. S.
,
2008
, “
Robust Output Feedback H∞ Control of Uncertain Markovian Jump Systems With Mode-Dependent Time-Delays
,”
Int. J. Control
,
81
(
1
), pp.
43
61
.10.1080/00207170701235766
38.
Li
,
H.
, and
Shi
,
Y.
,
2012
, “
Robust H∞ Filtering for Nonlinear Stochastic Systems With Uncertainties and Random Delays Modeled by Markov Chains
,”
Automatica
,
48
(
1
), pp.
159
166
.10.1016/j.automatica.2011.09.045
39.
Shen
,
M.
, and
Yang
,
G.
,
2012
, “
H2 Filter Design for Discrete Markov Jump Linear System With Partly Unknown Transition Probabilities
,”
Opt. Control Appl. Methods
,
33
(
3
), pp.
318
337
.10.1002/oca.998
40.
Cao
,
Y.
, and
Frank
,
M.
,
2000
, “
Robust H∞ Disturbance Attenuation for a Class of Uncertain Discrete-Time Fuzzy Systems
,”
IEEE Trans. Fuzzy Syst.
,
8
(
4
), pp.
406
415
.10.1109/91.868947
41.
Duan
,
Z.
,
Zhang
,
J.
,
Zhang
,
C.
, and
Mosca
,
E.
,
2006
, “
Robust H2 and H∞ Filtering for Uncertain Linear Systems
,”
Automatica
,
42
(
11
), pp.
1919
1926
.10.1016/j.automatica.2006.06.004
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