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Article: Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

TitleStability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions
Authors
Keywords2-D system
Basis-dependent Lyapunov function
Control design
Fuzzy system
Stability analysis
Issue Date2013
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0923-6082
Citation
Multidimensional Systems And Signal Processing, 2013, v. 24 n. 3, p. 395-415 How to Cite?
AbstractThis paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples. © 2011 The Author(s).
Persistent Identifierhttp://hdl.handle.net/10722/147107
ISSN
2015 Impact Factor: 1.436
2015 SCImago Journal Rankings: 0.768
References

Boyd S., ElGhaoui L., Feron E., Balakrishnan V. (1994) Linear matrix inequalities in systems and control theory. SIAM, Philadelphia, PA doi: 10.1137/1.9781611970777

Chen C. W., Tsai J. S. H., Shieh L. S. (1999) Two-dimensional discrete-continuous model conversion. Circuits, Systems and Signal Processing 18: 565–585 doi: 10.1007/BF01269917

Choi D., Park P. (2003) H ∞ state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions. IEEE Transaction on Fuzzy Systems 11: 271–278 doi: 10.1109/TFUZZ.2003.809903

de Oliveira M. C., Geromel J. C., Bernussou J. (2002) Extended H 2 and H ∞ norm characterizations and controller parametrizations for discrete-time systems. International Journal of Control 75: 666–679 doi: 10.1080/00207170210140212

Du C., Xie L. (1999) Stability analysis and stabilization of uncertain two-dimensional discrete systems: an LMI approach. IEEE Transactions on Circuits and Systems (I) 46(11): 1371–1374 doi: 10.1109/81.802835

Du C., Xie L., Soh Y. C. (2000) H ∞ filtering of 2-D discrete systems. IEEE Transactions on Signal Processing 48(6): 1760–1768 doi: 10.1109/78.845933

Du C., Xie L., Soh Y. C. (2001) H ∞ reduced-order approximation of 2-D digital filters. IEEE Transactions on Circuits and Systems (I) 48(6): 688–698 doi: 10.1109/81.928152

Fornasini E., Marchesini G. (1978) Doubly indexed dynamical systems: State-space models and structural properties. Mathematical Systems Theory 12: 59–72 doi: 10.1007/BF01776566

Gao H., Lam J., Xu S., Wang C. (2004) Stabilization and H ∞ control of two-dimensional Markovian jump systems. IMA Journal of Mathematics and Control Information 21(4): 377–392 doi: 10.1093/imamci/21.4.377

Gao H., Lam J., Xu S., Wang C. (2005) Stability and stabilization of uncertain 2-D discrete systems with stochastic perturbation. Multidimensional Systems and Signal Processing 16(1): 85–106 doi: 10.1007/s11045-004-4739-y

Gao H., Zhao Y., Lam J., Chen K. (2009) H ∞ fuzzy filtering of nonlinear systems with intermittent measurements. IEEE Transactions on Fuzzy Systems 17(2): 291–300 doi: 10.1109/TFUZZ.2008.924206

Guerra T. M., Vermeiren L. (2004) LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno’s form. Automatica 40(8): 823–829 doi: 10.1016/j.automatica.2003.12.014

Haddad M. W., Bernstein S. D. (1995) Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis. IEEE Transactions on Automatic Control 40(3): 536–543 doi: 10.1109/9.376077

Hinamoto T. (1997) Stability of 2-D discrete systems described by the Fornasini–Marchesini second model. IEEE Transactions on Circuits and Systems (I) 44(3): 254–257 doi: 10.1109/81.557373

Kim E., Kim S. (2002) Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI: Continuous case. IEEE Transactions on Fuzzy Systems 10(3): 391–400 doi: 10.1109/TFUZZ.2002.1006442

Kim E., Lee H. (2000) New approaches to relaxed quadratic stability condition of fuzzy control systems. IEEE Transactions on Fuzzy Systems 8(5): 523–534 doi: 10.1109/91.873576

Lam J., Zhou S. (2007) Dynamic output feedback H ∞ control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach. International Journal of Society Systems Science 38(1): 25–37 doi: 10.1080/00207720601042967

Lin Z., Lam J., Galkowski K., Xu S. (2001) A constructive approach to stabilizability and stabilization of a class of nD systems. Multidimensional Systems and Signal Processing 12(3–4): 329–343 doi: 10.1023/A:1011909707499

Liu D. (1998) Lyapunov stability of two-dimensional digital filters with overflow nonlinearities. IEEE Transactions on Circuits and Systems (I) 45(5): 574–577 doi: 10.1109/81.668870

Liu H., Sun F., Hu Y.N. (2005) H ∞ control for fuzzy singularly perturbed systems. Fuzzy Sets and Systems 155: 272–291 doi: 10.1016/j.fss.2005.05.004

Liu X., Zhang Q.L. (2003) New approaches to controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica 39: 1571–1582 doi: 10.1016/S0005-1098(03)00172-9

Lu W. M., Doyle J. C. (1995) H ∞ control of nonlinear systems: A convex characterization. IEEE Transactions on Automatic Control 40(9): 1668–1675 doi: 10.1109/9.412643

Lu W.S. (1994) On a Lyapunov approach to stability analysis of 2-D digital filters. IEEE Transactions on Circuits and Systems (I) 41(10): 665–669 doi: 10.1109/81.329727

Tuan H. D., Apkarian P., Nguyen T. Q. (2002) Robust mixed H 2/H ∞ filtering of 2-D systems. IEEE Transactions on Signal Processing 50(7): 1759–1771 doi: 10.1109/TSP.2002.1011215

Wang H. O., Tanaka K., Griffin M. (1996) An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Transactions on Fuzzy Systems 4(1): 14–23 doi: 10.1109/91.481841

Wu L., Ho D. W. C. (2009) Fuzzy filter design for nonlinear Itô stochastic systems with application to sensor fault detection. IEEE Transactions on Fuzzy System 17: 233–242 doi: 10.1109/TFUZZ.2008.2010867

Wu L., Shi P., Gao H., Wang C. (2008) H ∞ filtering for 2D Markovian jump systems. Automatica 44(7): 1849–1858 doi: 10.1016/j.automatica.2007.10.027

Wu L., Su X., Shi P., Qiu J. (2011) A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B 41: 273–286 doi: 10.1109/TSMCB.2010.2051541

Wu L., Wang Z., Gao H., Wang C. (2007) H ∞ and l 2-l ∞ filtering for two-dimensional linear parameter-varying systems. International Journal of Robust & Nonlinear Control 17(12): 1129–1154 doi: 10.1002/rnc.1169

Xie L., Du C., Soh Y. C., Zhang C. (2002) H ∞ and robust control of 2-D systems in FM second model. Multidimensional Systems and Signal Processing 13: 256–287 doi: 10.1023/A:1015808429836

Xu H., Zou Y., Xu S., Lam J., Wang Q. (2005) H ∞ model reduction of 2-D singular Roesser models. Multidimensional Systems and Signal Processing 16(3): 285–304 doi: 10.1007/s11045-005-1678-1

Yoneyama J. (2006) Robust H ∞ control analysis and synthesis for Takagi-Sugeno general uncertain fuzzy systems. Fuzzy Sets and Systems 57(16): 2205–2223 doi: 10.1016/j.fss.2006.03.020

Zhou S., Lam J., Xue A. (2007) H ∞ filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach. Fuzzy Sets and Systems 158(2): 180–193 doi: 10.1016/j.fss.2006.09.001

Zhou S., Li T. (2005) Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov-Krasovskii function. Fuzzy Sets and Systems 151(1): 139–153 doi: 10.1016/j.fss.2004.08.014

 

DC FieldValueLanguage
dc.contributor.authorChen, Xen_HK
dc.contributor.authorLam, Jen_HK
dc.contributor.authorGao, Hen_HK
dc.contributor.authorZhou, Sen_HK
dc.date.accessioned2012-05-28T08:17:26Z-
dc.date.available2012-05-28T08:17:26Z-
dc.date.issued2013en_HK
dc.identifier.citationMultidimensional Systems And Signal Processing, 2013, v. 24 n. 3, p. 395-415en_HK
dc.identifier.issn0923-6082en_HK
dc.identifier.urihttp://hdl.handle.net/10722/147107-
dc.description.abstractThis paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples. © 2011 The Author(s).en_HK
dc.languageengen_US
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0923-6082en_HK
dc.relation.ispartofMultidimensional Systems and Signal Processingen_HK
dc.rightsThe Author(s)en_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong Licenseen_US
dc.subject2-D systemen_HK
dc.subjectBasis-dependent Lyapunov functionen_HK
dc.subjectControl designen_HK
dc.subjectFuzzy systemen_HK
dc.subjectStability analysisen_HK
dc.titleStability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functionsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://www.springerlink.com/link-out/?id=2104&code=M835H4U8U720M51H&MUD=MPen_US
dc.identifier.emailLam, J:james.lam@hku.hken_HK
dc.identifier.authorityLam, J=rp00133en_HK
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1007/s11045-011-0166-zen_HK
dc.identifier.scopuseid_2-s2.0-84878220113en_HK
dc.identifier.hkuros236063-
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dc.relation.referencesDu C., Xie L., Soh Y. C. (2001) H ∞ reduced-order approximation of 2-D digital filters. IEEE Transactions on Circuits and Systems (I) 48(6): 688–698en_US
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dc.identifier.spage395en_HK
dc.identifier.epage415en_HK
dc.identifier.eissn1573-0824en_US
dc.publisher.placeUnited Statesen_HK
dc.description.otherSpringer Open Choice, 28 May 2012en_US
dc.identifier.scopusauthoridChen, X=54399871500en_HK
dc.identifier.scopusauthoridLam, J=7201973414en_HK
dc.identifier.scopusauthoridGao, H=7402971422en_HK
dc.identifier.scopusauthoridZhou, S=7404166480en_HK
dc.identifier.citeulike10054816-

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