Summary
Stability issues for switched systems whose subsystems are all fuzzy systems, either continuous-time or discrete-time, are studied and new results derived. Innovated representation models for switched fuzzy systems are proposed. The single Lyapunov function method has been adopted to study the stability of this class of switched fuzzy systems. Sufficient conditions for quadratic asymptotic stability are presented and stabilizing switching laws of the state–dependent form are designed. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.
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References
Berenji, H. R.: Fuzzy Logic Controllers. In: R. R. Yager and L. A. Zadeh (eds.): An Introduction to Fuzzy Logic Applications in Intelligent Systems. Kluwer Academic, Boston, MA (1993) 69–76.
Branicky, M. S.: Stability of Switched and Hybrid systems. In: Proceedings of the 34th IEEE Conference on Decision and Control, Lake Buena Vista, FL. The IEEE Press, Piscataway, NJ (1994) 3498–3503.
Branicky, M. S.: Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems. IEEE Transactions on Automatic Control 43, 4 (1998) 475–482.
Chen, C. L., Chang, M. H.: Optimal Design of Fuzzy Sliding Mode Control: A Comparative Study. Fuzzy Sets & Systems 93 (1998) 37–48.
Doo, J. C., PooGyeon, P.: State Feedback Controller Design for Discrete-Time Switching Fuzzy Systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NA (2002) paper A06 (1–6).
Doo, J. C., Seung, S. L., PooGyeon, P.: Output-Feedback H ∞ Control of Discrete-Time Switching Fuzzy Systems. In: Proceedings of the 2003 IEEE International Conference on Fuzzy Systems. The IEEE Press, Piscataway, NJ (2003) 441–446.
Doo, J. C., PooGyeon, P.: Guaranteed Cost Controller Design for Discrete-time Switching Fuzzy Systems. IEEE Transactions on Systems, Man & Cybernetics – Part A: Systems and Humans 34, 2 (2004) 110–119.
Johansson, M., Rantzer, A.: Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems. IEEE Transactions on Automatic Control 43, 4 (1998) 555–559.
Li, H. X., Gatland, H. B., Green, A. W.: Fuzzy Variable Structure Control. IEEE Transactions on Systems, Man & Cybernetics – Part B: Cybernetics 27, 2 (1997) 306–312.
Ooba, T., Funahashi, Y.: On a common quadratic Lyapunov functions for widely distant systems. IEEE Transactions on Automatic Control 42 (1997) 1697–1699.
Palm, R.: Sliding Mode Fuzzy Control. In: Proceedings of the 1992 IEEE International Conference on Fuzzy Systems. The IEEE Press, Piscataway, NJ (1992) 519–526.
Palm, R., Driankov, D.: Fuzzy Switched Hybrid Systems – Modelling and Identification. In: Proceedings of the 1998 IEEE International Conference on Fuzzy Systems, Gaithersburg, MD. The IEEE Press, Piscataway, NJ (1998) 130–135.
Pettersson, S., Lennartson, B.: Stability and Robustness for Hybrid Systems. In: Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, JP. The IEEE Press, Piscataway, NJ (1996) 1202–1207.
Savkin, A. V., Matveev, A. S.: Cyclic Linear Differential Automata: A Simple Class of Hybrid Dynamical Systems. Automatica 36, 5 (2000) 727–734.
Shim, H., Noh, D. J., Seo, J. H.: Common Lyapunov Function for Exponentially Stable Nonlinear Systems. Presented at the 4th SIAM Conf. on Control and Its Applications, Jacksonville, FL (1998) private communication.
Sugeno, M., Griffin, M. F., Bastian, A.: Fuzzy Hierarchical Control of an Unmanned Helicopter: In: Proceedings of the 5th IFSA World Congress, Seoul, KO. The International Fuzzy System Federation, Seoul, KO (1993) 1262–1265.
Systems and Control Encyclopaedia: Theory, Technology, Applications, M. G. Singh, Editor-in-Chief, In: Contributions on Nonlinear Systems, Vol. 5, Pergamon Press, Oxford, UK (1987) 3366–3383.
Takagi, T., Sugeno, M.: Fuzzy Identification of Systems and its Application to Modelling and Control. IEEE Transactions on Systems, Man & Cybernetics 15, 1 (1985) 116–132.
Tanaka, K., Sugeno, M.: Stability Analysis and Design of Fuzzy Control Systems. Fuzzy Set & Systems 45, 2 (1992) 135–156.
Tanaka, K., Masaaki, I., Hua, O. W.: Stability and Smoothness Conditions for Switching Fuzzy Systems: In: Proceedings of the 19th American Control Conference. The IEEE Press, Piscataway, NJ (2000) 2474–2478.
Varaiya, P. P.: Smart Cars on Smart Roads: Problems of Control. IEEE Transactions on Automatic Control 38, 2 (1993) 195–207.
Wang, H. O., Tanaka, K., Griffin, M.: Parallel Distributed Compensation of Nonlinear Systems by Takagi and Sugeno’s Fuzzy Model. In: Proceedings of the 1995 IEEE Fuzzy System Conference FUZZ-IEEE’95, Yokahoma, JP. The IEEE Press, Piscataway, NJ (1995) 4790–4795.
Wang, H. O., Tanaka, K., Griffin, M.: An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues. IEEE Transactions on Fuzzy Systems 4, 1 (1996) 14–23.
Ye, H., Michael, A. N.: Stability Theory for Hybrid Dynamical Systems. IEEE Transactions on Automatic Control 43, 4 (1998) 464–474.
Zhao, J., Dimirovski, G. M.: Quadratic Stability for a Class of Switched Nonlinear Systems. IEEE Transactions on Automatic Control 49, 4 (2004) 574–578.
Dimirovski, G. M.: Lyapunov Stability in Control Synthesis Design Using Fuzzy-Logic and Neural-Networks. In: P. Borne, M. Benrejep, N. Dangoumau, and L. Lorimer (eds.): Proceedings of the 17th IMACS World Congress, Paris, July 11–15. The IMACS and Ecole Centrale de Lille, Villeneuve d’Ascq, FR (2005) Paper T5-I-01-0907, 1–8.
The MathWorks, Matlab Control Toolbox, Fuzzy Toolbox, LMI Tooolbox, and Simulink. The MathWorks Inc, Natick, MA (1999).
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Yang, H., Dimirovski, G.M., Zhao, J. (2008). Switched Fuzzy Systems: Representation Modelling, Stability Analysis, and Control Design. In: Chountas, P., Petrounias, I., Kacprzyk, J. (eds) Intelligent Techniques and Tools for Novel System Architectures. Studies in Computational Intelligence, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77623-9_9
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DOI: https://doi.org/10.1007/978-3-540-77623-9_9
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