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This study is concerned with the problem of robust H 2 and H ∞ filtering for uncertain discrete-time linear systems. Two types of time-invariant parametric uncertainty, namely polytopic and ellipsoidal, are considered and represented by a linear fractional transformation structure. Obtained auxiliary variables by a convex optimisation problem, play the role of decoupling the Lyapunov variables and the robust filter parameters, in order to cast the problem into a linear matrix inequality-based optimisation problem. The design conditions are derived based on the quadratic separation concept and employing appropriate parameterisations for the corresponding set of multipliers. The merit of the methods presented in this study lies in their less conservatism than the existing methods for the polytopic uncertain systems, as well as presenting a new convex optimisation procedure for the robust filtering for the ellipsoidal uncertain systems.
References
-
-
1)
-
5. de Souza, C.E., Trofino, A.: ‘A linear matrix inequality approach to the design of robust H2 filters’, in Ghaoui, L.E., Niculescu, S.I. (Eds.): ‘Advances in linear matrix inequality methods in control’, (SIAM, Philadelphia, 2000), pp. 175–185.
-
2)
-
M.C. de Oliveira ,
J. Bernussou ,
J.C. Geromel
.
A new discrete-time robust stability condition.
Syst. Control Lett.
,
261 -
265
-
3)
-
J.C. Geromel ,
J. Bernussou ,
G. Garcia ,
M.C. de Oliveira
.
H2 and H∞ robust filtering for discrete-time linear systems.
SIAM J. Control Optim.
,
5 ,
1353 -
1368
-
4)
-
H.D. Tuan ,
P. Apkarian ,
T.Q. Nguyen
.
Robust and reduced-order filtering: new LMI-based characterizations and methods.
IEEE Trans. Signal Proc.
,
12 ,
2975 -
2984
-
5)
-
25. Barenthin, M., Bombois, X., Hjalmarsson, H., Scorletti, G.: ‘Identification for control of multivariable systems: controller validation and experiment design via LMIs’, Automatica, 2008, 44, pp. 3070–3078 (doi: 10.1016/j.automatica.2008.05.022).
-
6)
-
1. Bombois, X., Hjalmarsson, H., Scorletti, G.: ‘Identification for robust H2 deconvolution filtering’, Automatica, 2010, 46, pp. 577–584 (doi: 10.1016/j.automatica.2010.01.023).
-
7)
-
39. Oliveira, M.C., Skelton, R.E.: ‘Stability tests for constrained linear systems’. , Moheimani, S., (Ed.): ‘ser. Lecture Notes in Control and Information Sciences’, (Springer, London, 2001), vol. 268, pp. 241–257.
-
8)
-
L. Xie ,
L. Lu ,
D. Zhang ,
H. Zhang
.
Improved robust ℋ2 and ℋ∞ filtering for uncertain discrete-time systems.
Automatica
,
873 -
880
-
9)
-
3. Zhou, K., Doyle, J.C., Glover, K.: ‘Robust and optimal control’ (Prentice-Hall, Englewood Cliffs, NJ, 1995).
-
10)
-
K.A. Barbosa ,
C.E. de Souza ,
A. Trofino
.
Robust ℋ2 filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions.
Syst. Control Lett.
,
3 ,
251 -
262
-
11)
-
D. Peaucelle ,
D. Arzelier
.
Robust performance analysis with LMI-based methods for real parametric uncertainty via parameter-dependent Lyapunov functions.
IEEE Trans. Autom. Control
,
4 ,
624 -
630
-
12)
-
24. Sadeghzadeh, A.: ‘Performance analysis for uncertain multivariable systems obtained by system identification’, Int. J. Syst. Sci., 2014, 45, (3), pp. 547–555 (doi: 10.1080/00207721.2012.724105).
-
13)
-
2. Scherer, C.W., Köse, I.E.: ‘Robustness with dynamic IQCs: an exact state-space characterization of nominal stability with applications to robust estimation’, Automatica, 2008, 44, pp. 1666–1675 (doi: 10.1016/j.automatica.2007.10.023).
-
14)
-
E.N. Goncalves ,
R.M. Palhares ,
R.H.C. Takahashi
.
H2/H∞ filter design systems with polytopic-bounded uncertainty.
IEEE Trans. Signal Process.
,
3620 -
3626
-
15)
-
19. Geromel, J.C., Korogui, R.H.: ‘H2 robust filter design with performance certificate via convex programming’, Automatica, 2004, 44, (4), pp. 937–948 (doi: 10.1016/j.automatica.2007.08.010).
-
16)
-
D. Peaucelle ,
D. Arzelier ,
O. Bachelier ,
J. Bernussou
.
A new robust -stability condition for real convex polytopic uncertainty.
Syst. Control Lett.
,
1 ,
21 -
30
-
17)
-
28. Sadeghzadeh, A., Momeni, H., Karimi, A.: ‘Fixed-order H∞ controller design for systems with ellipsoidal parametric uncertainty’, Int. J. Control, 2011, 84, (1), pp. 57–65 (doi: 10.1080/00207179.2010.540040).
-
18)
-
J. Geromel ,
M. De Oliveira
.
ℋ2 and ℋ∞ robust filtering for convex bounded uncertain systems.
IEEE Trans. Autom. Control
,
1 ,
100 -
107
-
19)
-
H.J. Gao ,
J. Lam ,
L.H. Xie ,
C.H. Wang
.
New approach to mixed H2/H∞ filtering for polytopic discrete-time systems.
IEEE Trans. Signal Process.
,
3183 -
3192
-
20)
-
T. Iwasaki ,
S. Hara
.
Well-posedness of feedback systems: insights into exact robustness analysis and approximate computations.
IEEE Trans. Autom. Control AC
,
5 ,
619 -
630
-
21)
-
22. Scherer, C.: ‘A full block S-procedure with applications’. 36th IEEE Conf. on Decision and Control, San Diego, CA, December 1997.
-
22)
-
37. Sadeghzadeh, A., Momeni, H.: ‘Fixed-order robust H∞ control and control-oriented uncertainty set shaping for systems with ellipsoidal parametric uncertainty’, Int. J. Robust Nonlinear Control, 2011, 21, pp. 648–665 (doi: 10.1002/rnc.1614).
-
23)
-
Oliveria M.C. de ,
J.C. Geromel ,
J. Bernussou
.
Extended H2 and H∞ norm characterizations and controller parameterizations for discrete-time systems.
Int. J. Control
,
666 -
679
-
24)
-
M.J. Lacerda ,
R.C.L.F. Oliveira ,
P.L.D. Peres
.
Robust H2 and H∞ filter design for uncertain linear systems via LMIs and polynomial matrices.
Signal Process.
,
5 ,
1115 -
1122
-
25)
-
I. Yaesh ,
U. Shaked
.
LMI approach to the mixed ℋ2/ℋ∞ filtering design for discrete-time uncertain systems.
IEEE Trans. Aerosp. Electron. Syst.
,
1 ,
292 -
296
-
26)
-
J.C. Geromel
.
Optimal linear filtering with parameter uncertainty.
IEEE Trans. Signal Process.
,
168 -
175
-
27)
-
38. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: ‘Linear matrix inequalities in system and control theory’ (SIAM, Philadelphia, 1994).
-
28)
-
H. Gao ,
X. Meng ,
T. Chen
.
ℋ∞ filter design for discrete delay systems: a new parameter-dependent approach.
Int. J. Control
,
6 ,
993 -
1005
-
29)
-
23. Ljung, L.: ‘System identification – theory for the user’ (Prentice-Hall, NJ, USA, 1999, 2nd edn.).
-
30)
-
Z. Duan ,
J. Zhang ,
C. Zhang ,
E. Mosca
.
Robust H2 and H∞ filtering for uncertain linear systems.
Automatica
,
11 ,
1919 -
1926
-
31)
-
26. Helmerson, A.: ‘Paramter-dependent Lyapunov functions based on linear fractional transformations’. 14th IFAC World Congress, Beijing, 1999.
-
32)
-
36. Agulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D.: ‘Robust H∞ static output-feedback design for time-invariant discrete-time polytopic systems from parameter-dependent state-feedback gains’. American Control Conf. (ACC), 2010, Baltimore, MD, USA, 2010.
-
33)
-
H. Gao ,
X. Meng ,
T. Chen
.
A new design of robust H2 filters for uncertain systems.
Syst. Control Lett.
,
7 ,
585 -
593
-
34)
-
K. Sun ,
A. Packard
.
Robust H2 and H∞ filters for uncertain LFT systems.
IEEE Trans. Autom. Control
,
5 ,
715 -
720
-
35)
-
33. Löfberg, J.: ‘YALMIP: A toolbox for modeling and optimization in MATLAB’. CACSD Conference, 2004. .
-
36)
-
34. Toh, K.C., Todd, M.J., Tutuncu, R.H.: ‘SDPT3: a MATLAB software package for semidefinite programming’, Optim. Methods Softw., 1999, 11, pp. 545–581 (doi: 10.1080/10556789908805762).
-
37)
-
J.C. Geromel ,
M.C. de Oliveira ,
J. Bernussou
.
Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions.
SIAM J. Control Optim.
,
3 ,
700 -
711
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