Abstract
The article is interested MR problem for continuous T-S systems. Sufficient conditions are then established for the error system (ES) are asymptotically stable (AS) has L2-gain performance. An example is provided to check effectiveness of the derived results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wang, Q., Lam, J.: Optimal H2 model reduction for mechanical systems. Int. J. Innov. Comput. Inf. Control 6(5), 2045–2054 (2010)
Xu, S., Chen, T.: H∞ model reduction in the stochastic framework. SIAM J. Control Optim. 42(4), 1293–1309 (2003)
Glover, K.: All optimal Hankel-norm approximations of linear multivariable systems and their L∞ error bounds. Int. J. Control 39(6), 1115–1195 (1984)
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994)
Wang, Q., Lam, J., Xu, S., Gao, H.: Delay dependent and delay independent energy-to-peak model approximation for systems with time-varying delay. Int. J. Syst. Sci. 36(8), 445–460 (2005)
Zhang, L., Huang, B., Lam, J.: H∞ model reduction of Markovian jump linear systems. Int. J. Control 78(15), 1198–1205 (2005)
Wu, L., Su, X., Shi, P., Qiu, J.: Model approximation for discrete-time statedelay systems in the T-S fuzzy framework. IEEE Trans. Fuzzy Syst. 19(2), 366–378 (2011)
Su, X., Wu, L., Shi, P., Song, Y.-D.: H∞ model reduction of Takagi-Sugeno fuzzy stochastic systems. IEEE Trans. Systems Man Cybern.-Part B: Cybern. 42(6), 1574–1585 (2012)
Yoo, S.-H., Choi, B.-J.: A balanced model reduction for T-S fuzzy systems with uncertain time varying parameters. In: Zhang, J., He, J.-H., Fu, Y. (eds.) CIS 2004. LNCS, vol. 3314, pp. 148–153. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30497-5_24
Feng, G.: A survey on analysis and design of model-based fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(5), 676–697 (2006)
Kim, E., Lee, H.: New approaches to relaxed quadratic stability condition of fuzzy control systems. IEEE Trans. Fuzzy Syst. 8(5), 523–534 (2000)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC-15(1), 116–132 (1985)
Nguang, S.K., Assawinchaichote, W.: H∞ filtering for fuzzy dynamical systems with D-stability constraints. IEEE Trans. Circuits Syst. I Reg. Pap. 50(11), 1503–1508 (2003)
El-Amrani, A., Boumhidi, I., Boukili, B., Hmamed, A.: A finite frequency range approach to H∞ filtering for TS fuzzy systems. Procedia Comput. Sci. 148, 485–494 (2019)
Gahinet, P., Apkarian, P.: A linear matrix inequality approach to H∞ control. Int. J. Robust Nonlinear Control 4(4), 421–448 (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Lahlou, Z., El-Amrani, A., Boumhidi, I. (2022). Model Reduction in Takagi Sugeno Systems: An LMI Method. In: Motahhir, S., Bossoufi, B. (eds) Digital Technologies and Applications. ICDTA 2022. Lecture Notes in Networks and Systems, vol 454. Springer, Cham. https://doi.org/10.1007/978-3-031-01942-5_79
Download citation
DOI: https://doi.org/10.1007/978-3-031-01942-5_79
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-01941-8
Online ISBN: 978-3-031-01942-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)