© The Institution of Engineering and Technology
This study is concerned with the generalised ℋ2 fault detection problem for a class of discrete-time switched systems with repeated scalar non-linearities. To reduce the overdesign of the quadratic framework, this study proposes a switching-sequence-dependent Lyapunov function approach to the fault detection filter design procedure. Sufficient conditions are obtained for the existence of admissible generalised ℋ2 fault detection filter. Since these conditions involve matrix equalities, the cone complementarity linearisation procedure is employed to cast the non-convex feasibility problem into a sequential minimisation problem subject to linear matrix inequalities, which can be readily solved by using the standard numerical software. If these conditions are feasible, a desired fault detection filter can be easily constructed. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory.
References
-
-
1)
-
10. Wu, L., Lam, J.: ‘Sliding mode control of switched hybrid systems with time-varying delay’, Int. J. Adapt. Control Signal Process., 2008, 22, (10), pp. 909–931 (doi: 10.1002/acs.1030).
-
2)
-
P. Shi ,
E.K. Boukas ,
K. Agarwal
.
Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay.
IEEE Trans. Autom. Control
,
11 ,
2139 -
2144
-
3)
-
H. Gao ,
T. Chen ,
L. Wang
.
Robust fault detection with missing measurements.
Int. J. Control
,
5 ,
804 -
819
-
4)
-
15. Beck, C., D’Andrea, R., Paganini, F., Lu, W.M., Doyle, J.: ‘A state-space theory of uncertain systems’. Proc. 13th Triennial IFAC World Congress, San Francisco, CA, 1996, pp. 291–296.
-
5)
-
11. Wu, L., Zheng, W.X.: ‘ℋ∞ model reduction for switched hybrid systems with time-varying delay’, Automatica, 2009, 45, (1), pp. 186–193 (doi: 10.1016/j.automatica.2008.06.024).
-
6)
-
12. Chu, Y.C., Glover, K.: ‘Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities’, IEEE Trans. Autom. Control, 1999, 44, (3), pp. 471–483 (doi: 10.1109/9.751342).
-
7)
-
J. Daafouz ,
P. Riedinger ,
C. Iun
.
Stability analysis and control synthesis for switched systems: a switched lyapunov function approach.
IEEE Trans. Autom. Control
,
11 ,
1883 -
1887
-
8)
-
5. Liberzon, D.: ‘Switching in systems and control’ (Birkhauser, Boston, 2003).
-
9)
-
L.E. Ghaoui ,
F. Oustry ,
M. AitRami
.
A cone complementarity linearization algorithm for static output-feedback and related problems.
IEEE Trans. Autom. Control
,
8 ,
1171 -
1176
-
10)
-
20. Jiang, B., Staroswiecki, M., Cocquempot, V.: ‘ℋ∞ fault detection filter design for linear discrete-time systems with multiple time delays’, Int. J. Syst. Sci., 2003, 34, (5), pp. 365–373 (doi: 10.1080/00207720310001601037).
-
11)
-
M. Sun ,
J. Zhao ,
D.J. Hill
.
Stability and ℒ2 gain for switched delay systems: a delay-dependent method.
Automatica
,
10 ,
1769 -
1774
-
12)
-
L.Q. Wu ,
D.W.C. Ho
.
Fuzzy filter design for Ito stochastic systems with application to sensor detection.
IEEE Trans. Fuzzy Syst.
,
1 ,
233 -
242
-
13)
-
L. Hetel ,
J. Daafouz ,
C. Iung
.
Stabilization of arbitrary switched linear systems with unknown time-varying delays.
IEEE Trans. Automatic Control
,
10 ,
1668 -
1674
-
14)
-
13. Chu, Y.C., Glover, K.: ‘Stabilization and performance synthesis for systems with repeated scalar nonlinearities’, IEEE Trans. Autom. Control, 1999, 44, (3), pp. 484–496 (doi: 10.1109/9.751343).
-
15)
-
1. Hespanha, J.P., Morse, A.S.: ‘Stability of switched systems with average dwell time’. Proc. 38th Conf. Decision Control, Phoenix, AZ, 1999, pp. 2655–2660.
-
16)
-
26. Wang, Z., Shen, B., Shu, H., Wei, G.: ‘Quantized ℋ∞ control for nonlinear stochastic time-delay systems with missing measurements’, IEEE Trans. Autom. Control, 2012, 57, (6), pp. 1431–1444 (doi: 10.1109/TAC.2011.2176362).
-
17)
-
P. Gahinet ,
P. Apkarian
.
A linear matrix inequality approach to H∞ control.
Int. J. Robust Nonlinear Control
,
421 -
448
-
18)
-
16. Albertini, F., Sontag, E.D.: ‘State observability in recurrent neural networks’, Syst. Control Lett., 1994, 22, pp. 235–244 (doi: 10.1016/0167-6911(94)90054-X).
-
19)
-
H. Ishii ,
B.A. Francis
.
Stabilizing a linear system by switching control with dwell time.
IEEE Trans. Autom. Control
,
12 ,
1962 -
1973
-
20)
-
24. Gahinet, P., Nemirovskii, A., Laub, A.J., Chilali, M.: ‘LMI control toolbox users guide’ (The MathWorks, Natick, MA, 1995).
-
21)
-
S.K. Nguang ,
P. Shi ,
S. Ding
.
Fault detection for uncertain fuzzy systems: an LMI approach.
IEEE Trans. Fuzzy Syst.
,
1251 -
1262
-
22)
-
M. Zhong ,
S.X. Ding ,
J. Lam ,
H. Wang
.
An LMI approach to design robust fault detection filter for uncertain LTI systems.
Automatica
,
543 -
550
-
23)
-
L. Wu ,
P. Shi ,
H. Gao ,
C. Wang
.
ℋ∞ filtering for 2D Markovian jump systems.
Automatica
,
7 ,
1849 -
1858
-
24)
-
M. Zhong ,
H. Ye ,
P. Shi ,
G. Wang
.
Fault detection for Markovian jump systems.
IEE Proc. Control Theory Appl.
,
4 ,
397 -
402
-
25)
-
H. Gao ,
J. Lam ,
C. Wang
.
Induced l2 and generalized ℋ2 filtering for systems with repeated scalar nonlinearities.
IEEE Trans. Signal Process.
,
11 ,
4215 -
4226
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.0463
Related content
content/journals/10.1049/iet-cta.2013.0463
pub_keyword,iet_inspecKeyword,pub_concept
6
6