Robust mixed ℋ2/ℋ∞ filtering design for discrete-time switched polytopic linear systems
Robust mixed ℋ2/ℋ∞ filtering design for discrete-time switched polytopic linear systems
- Author(s): J. Qiu ; G. Feng ; J. Yang
- DOI: 10.1049/iet-cta:20070289
For access to this article, please select a purchase option:
Buy article PDF
Buy Knowledge Pack
IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.
Thank you
Your recommendation has been sent to your librarian.
- Author(s): J. Qiu 1 ; G. Feng 2 ; J. Yang 3
-
-
View affiliations
-
Affiliations:
1: Department of Manufacturing Engineering and Engineering Management, University of Science and Technology of China and City University of Hong Kong Joint Advanced Research Center, Suzhou, People's Republic of China
2: Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong
3: Department of Precision Machinery and Instrumentation, University of Science and Technology of China, Hefei, People's Republic of China
-
Affiliations:
1: Department of Manufacturing Engineering and Engineering Management, University of Science and Technology of China and City University of Hong Kong Joint Advanced Research Center, Suzhou, People's Republic of China
- Source:
Volume 2, Issue 5,
May 2008,
p.
420 – 430
DOI: 10.1049/iet-cta:20070289 , Print ISSN 1751-8644, Online ISSN 1751-8652
The authors deal with mode and parameter-dependent robust mixed ℋ2/ℋ∞ filtering design for a class of discrete-time switched polytopic linear systems. The objective is to design a homogeneous switched mixed ℋ2/ℋ∞ filter guaranteeing the asymptotic stability of the resulting filtering error systems with given performance measures. Based on a switched parameter-dependent Lyapunov function combined with Finsler's lemma, some novel conditions for robust ℋ2 and ℋ∞ performance analysis are proposed and in turn the filter synthesis is developed. It is shown that by using a new linearisation technique combined with a bounding approach, the filter gains can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.
Inspec keywords: time-varying systems; linear systems; discrete time systems; Lyapunov methods; H∞ control; asymptotic stability; linear matrix inequalities
Other keywords:
Subjects: Optimal control; Stability in control theory; Discrete control systems; Algebra; Time-varying control systems
References
-
-
1)
- M.C. De Oliveira , R.E. Skelton , S.O. Reza Moheimani . (2001) Stability tests for constrained linear systems’, in Perspectives in robust control, Lecture Notes in Control and Information Scieneces.
-
2)
- L. Zhang , P. Shi , E.-K. Boukas , C. Wang . Robust l2−l∞ filtering for switched linear discrete time-delay systems with polytopic uncertainties. IET Control Theory Appl. , 3 , 722 - 730
-
3)
- R.M. Palhares , P.L.D. Peres . Robust filtering with guaranteed energy-to-peak performance–an LMI approach. Automatica , 6 , 851 - 858
-
4)
- Gao, H., Zhang, L., Shi, P., Mou, S., Wang, C.: `Stability and stabilization of switched linear discrete-time systems with polytopic uncertainties', Proc. 2006 American Control Conf., 2006, Minnesota, USA, p. 5953–5958.
-
5)
- H. Li , M. Fu . A linear matrix inequality approach to robust ℋ∞ filtering. IEEE Trans. Signal Process. , 9 , 2338 - 2350
-
6)
- W. Zhang , L. Yu , X. Jiang . Delay-dependent generalized ℋ2 filtering for uncertain systems with multiple time-varying state delays. Signal Process. , 4 , 709 - 724
-
7)
- R.C.L.F. Oliveira , P.L.D. Peres . LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions. Syst. Control Letters. , 1 , 52 - 61
-
8)
- E.N. Goncalves , R.M. Palhares , R.H.C. Takahashi , R.C. Mesquita . New strategy for robust stability analysis of discrete-time uncertain systems. Syst. Control Lett. , 516 - 524
-
9)
- H. Gao , J. Lam , P. Shi , C. Wang . Parameter-dependent filter design with guaranteed ℋ∞ performance. IEE Proc., Control Theory Appl. , 5 , 531 - 537
-
10)
- Fang, L., Lin, H., Antsaklis, P.J.: `Stabilization and performance analysis for a class of switched systems', Proc. 43rd IEEE Conf. Decision and Control, 2004, p. 3265–3270.
-
11)
- C.E. De Souza , K.A. Barbosa , A.T. Neto . Robust ℋ∞ filtering for discrte-time linear systems with uncertain time-varying parameters. IEEE Trans. Signal Process. , 6 , 2110 - 2118
-
12)
- H. Gao , J. Lam , L. Xie , C. Wang . New approach to mixed ℋ2/ℋ∞ filtering for polytopic discrete-time systems. IEEE Trans. Signal Process. , 8 , 3183 - 3192
-
13)
- E.N. Goncalves , R.M. Palhares , R.H.C. Takahashi . ℋ2/ℋ∞ filter design for systems with polytope-bounded uncertainty. IEEE Trans. Signal Process. , 9 , 3620 - 3626
-
14)
- Z. Duan , J. Wang , L. Huang . Parameter-dependent Lyapunov function method for a class of uncertain nonlinear systems with multiple equilibria. Circuits Syst. Signal Process. , 2 , 147 - 164
-
15)
- D. Du , B. Jiang , P. Shi , S. Zhou . ℋ∞ filtering of discrete-time switched systems with state delays via switched Lyapunov function approach. IEEE Trans. Autom. Control , 8 , 1520 - 1525
-
16)
- Z. Duan , J. Zhang , C. Zhang , E. Mosca . Robust ℋ2 and ℋ∞ filtering for uncertain linear systems. Automatica , 11 , 1919 - 1926
-
17)
- H. Rotstein , M. Sznaier , M. Idan . ℋ2/ℋ∞ filtering theory and an aerospace application. Int. J. Robust Nonlinear Control , 4 , 347 - 366
-
18)
- H. Gao , T. Chen . ℋ∞ estimation for uncertain systems with limited communication capacity. IEEE Trans. Autom. Control , 11 , 2070 - 2084
-
19)
- H. Gao , J. Lam , C. Wang . Model simplification for switched hybrid systems. Syst. Control Lett. , 12 , 1015 - 1021
-
20)
- J. Qiu , G. Feng , J. Yang . Improved delay-dependent ℋ∞ filtering design for discrete-time polytopic linear delay systems. IEEE Trans. Circuits Syst. II, Express Briefs, to appear
-
21)
- L. Zhang , P. Shi , C. Wang , H. Gao . Robust ℋ∞ filtering for switched linear discrete-time systems with polytopic uncertainties. Int. J. Adaptive Control Signal Process. , 6 , 291 - 304
-
22)
- E.N. Goncalves , R.M. Palhares , R.H.C. Takahashi , R.C. Mesquita . ℋ2 and ℋ∞ ε-guaranteed cost computation of uncertain linear systems. IET Control Theory Appl. , 1 , 201 - 209
-
23)
- R.A. Decarlo , M.S. Branchy , S. Pettersson , B. Lennartson . Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE , 7 , 1069 - 1082
-
24)
- R.M. Palhares , P.L.D. Peres . LMI approach to the mixed ℋ2/ℋ∞ filtering design for discrete-time systems. IEEE Trans. Aerosp. Electron. Sys. , 1 , 292 - 296
-
25)
- M.S. Branicky . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control , 4 , 475 - 482
-
26)
- H. Ye , A.N. Michel , L. Hou . Stability theory for hybrid dynamical systems. IEEE Trans. Autom. Control , 4 , 461 - 474
-
27)
- Z. Duan , J. Zhang , C. Zhang , E. Mosca . A simple design method of reduced-order filters and its applications to multirate filter bank design. Signal Process. , 5 , 1061 - 1075
-
28)
- L. Xie , L. Lu , D. Zhang , H. Zhang . Improved robust ℋ2 and ℋ∞ filtering for uncertain discrete-time systems. Automatica , 5 , 873 - 880
-
29)
- Z. Wang , D.W.C. Ho , X. Liu . Robust filtering under randomly varying sensor delay with variance constraints. IEEE Trans. Circuits Syst. II, Express Briefs , 6 , 320 - 326
-
30)
- D. Xie , L. Wang , F. Hao , G. Xie . LMI approach to L2-gain analysis and control synthesis of uncertain switched systems. IEE Proc. Control Theory Appl. , 1 , 21 - 28
-
31)
- D. Liberzon , A.S. Morse . Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. , 5 , 59 - 70
-
32)
- C. Farges , D. Peaucelle , D. Arzelier , J. Daafouz . Robust ℋ2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. Syst. Control Lett. , 2 , 159 - 166
-
33)
- H.D. Tuan , P. Apkarian , T.Q. Nguyen . Robust and reduced-order filtering: new LMI-based characterizations and methods. IEEE Trans. Signal Process. , 12 , 2975 - 2984
-
34)
- J. Daafouz , P. Riedinger , C. Iung . Stability and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Autom. Control , 11 , 1883 - 1887
-
35)
- G. Chesi , A. Garulli , A. Tesi , A. Vicino . Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions. Automatica , 2 , 309 - 316
-
36)
- Peleties, P., Decarlo, R.A.: `Asymptotic stability of m-switched systems using Lyapunov-like functions', Proc. 1991 American Control Conf, 1991, Boston, MA, p. 1679–1684.
-
37)
- Leite, V.J.S., Montagner, V.F., Peres, P.L.D.: `Robust pole location by parameter-dependent state feedback control', Proc. 41st IEEE Conf. Decision and Control, 2002, Las Vegas, NV, p. 1864–1869.
-
1)