Abstract
This paper deals with the problem of stabilizing the fuzzy interconnected bilinear systems via the state-feedback controllers with actuator saturation. Firstly, the nonlinear interconnected systems with the additive disturbance inputs are represented into the bilinear interconnected systems via Taylors series expansion and then we adopt the T-S fuzzy modeling technique to construct the fuzzy bilinear models. Secondly, the saturated linear state-feedback controllers for fuzzy interconnected bilinear systems are presented. An ellipsoid is the contractively invariant set of the fuzzy interconnected bilinear systems. The LMI-based conditions are proposed such that the fuzzy interconnected bilinear systems are asymptotically stable with the H ∞ performance with the ellipsoid contained in the region of attraction. Moreover, an assigned polytopic region of the state space, containing the equilibrium, is enclosed into the region of attraction of the equilibrium itself. Finally, a numerical example is utilized to demonstrate the validity and effectiveness of the proposed method.
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References
Chen, B., Liu, X.P.: Delay-Dependent Robust Control for T-S fuzzy systems with time delay. IEEE Trans. Fuzzy Systems 13, 544–556 (2005)
Cao, Y.Y., Frank, P.M.: Analysis and Synthesis of Nonlinear Time Delay Systems via Fuzzy Control. IEEE Trans. Fuzzy Systems 8, 200–211 (2000)
Wang, W.J., Luoh, L.: Stability and Stabilization of Fuzzy Large-Scale Systems. IEEE Trans. Fuzzy Systems 12, 309–315 (2004)
Xu, S., Lam, J.: Robust H ∞ Control for Uncertain Discrete-Time-Delay Fuzzy Systems via Output Feedback Controllers. IEEE Trans. Fuzzy Systems 13, 82–93 (2005)
Mohler, R.R.: Bilinear Control Processes. Academic Press, New York (1973)
Elliott, D.L.: Bilinear Systems in Encyclopedia of Electrical Engineering. Wiley, New York (1999)
Benallou, A., Mellichamp, D.A., Seborg, D.E.: Optimal Stabilizing Controllers for Bilinear Systems. Int. J. Contr. 48, 1487–1501 (1988)
Chen, M.S.: Exponential Stabilization of a Constrained Bilinear System. Automatica 34, 989–992 (1998)
Li, T.H., Tsai, S.H., Lee, J.Z.: Robust H ∞ Fuzzy Control for a Class of Uncertain Discrete Fuzzy Bilinear Systems. IEEE Trans. Syst. Man, Cybern. Part B 38, 510–527 (2008)
Hua, T.S., Lin, Z.L., Chen, B.M.: An Analysis and Design Method for Linear Systems Subject to Actuator Saturation and Disturbance. Automatica 38, 351–359 (2002)
Cao, Y.Y., Lin, Z.L.: Robust Stability Analysis and Fuzzy-Scheduling Control for Nonlinear Systems Subject to Actuator Saturation. IEEE Trans. Fuzzy Systems 11, 57–67 (2003)
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
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© 2012 Springer-Verlag Berlin Heidelberg
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Liu, X., Yang, D., Li, Z. (2012). New Robust H ∞ Fuzzy Control for the Interconnected Bilinear Systems Subject to Actuator Saturation. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds) Advances in Neural Networks – ISNN 2012. ISNN 2012. Lecture Notes in Computer Science, vol 7368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31362-2_42
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DOI: https://doi.org/10.1007/978-3-642-31362-2_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31361-5
Online ISBN: 978-3-642-31362-2
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