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Exponential estimates of a class of time-delay nonlinear systems with convex representations

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Języki publikacji
EN
Abstrakty
EN
This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.
Rocznik
Strony
815--826
Opis fizyczny
Bibliogr. 56 poz., rys., wykr.
Twórcy
autor
  • Research Center on Information Technology and Systems, Hidalgo State University, Carretera Pachuca-Tulancingo Km. 4.5, CP 42184, Mineral de la Reforma, Hidalgo, Mexico
  • Research Center on Information Technology and Systems, Hidalgo State University, Carretera Pachuca-Tulancingo Km. 4.5, CP 42184, Mineral de la Reforma, Hidalgo, Mexico
autor
  • Department of Electric and Electronics Engineering, Sonora Institute of Technology, 5 de Febrero 818 Sur, CP 85000, Ciudad Obregón, Sonora, Mexico
autor
  • Department of Electric and Electronics Engineering, Sonora Institute of Technology, 5 de Febrero 818 Sur, CP 85000, Ciudad Obregón, Sonora, Mexico
Bibliografia
  • [1] Ahmed, Q., Bhatti, A. and Iqbal, S. (2009). Robust decoupling control design for twin rotor system using Hadamard weights, Control Applications, (CCA) Intelligent Control, (ISIC), 2009 IEEE, St. Petersburg, Russia, pp. 1009–1014.
  • [2] Anderson, R.J. and Spong, M.W. (1989). Bilateral control of teleoperators with time delay, IEEE Transactions on Automatic Control 34(1): 494–501.
  • [3] Balasubramaniam, P., Lakshmanan, S. and Rakkiyappan, R. (2012). LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties, International Journal of Applied Mathematics and Computer Science 22(2): 339–351, DOI: 10.2478/v10006-012-0025-6.
  • [4] Beard, W.B., McLain, T.W., Nelson, D.B., Kingston, D. and Johanson, D. (2006). Decentralized cooperative aerial surveillance using fixed-wing miniature UAVs, Proceedings of the IEEE 94(1): 1306–1324.
  • [5] Bellman, R. and Cooke, K. (1963). Differential-Difference Equations, Academic Press, New York, NY.
  • [6] Boyd, S., Ghaoui, L.E., Feron, E. and Belakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, Vol. 15, SIAM, Philadelphia, PA.
  • [7] Cao, Y.Y. and Frank, P.M. (2001). Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models, Fuzzy Sets and Systems 124(2): 213–229.
  • [8] Chang, Y.C., Chen, S., Su, S. and Lee, T. (2004). Static output feedback stabilization for nonlinear interval time-delay systems via fuzzy control approach, Fuzzy Sets and Systems 148(3): 395–410.
  • [9] Chen, B., Lin, C., Liu, X. and Tong, S. (2007a). Guaranteed cost control of T–S fuzzy systems with input delay, International Journal of Robust Nonlinear Control 18(1): 1230–1256.
  • [10] Chen, B., Liu, X.and Tong, S. and Lin, C. (2007b). Guaranteed cost control of T–S fuzzy systems with state and input delays, Fuzzy Sets and Systems 158(20): 2251–2267.
  • [11] Chen, B. and Liu, X. (2005). Fuzzy guaranteed cost control for nonlinear systems with time-varying delay, IEEE Transactions on Fuzzy Systems 13(2): 238–249.
  • [12] Cheong, Niculescu, S.-I., Annaswamy, A. and Srinivasan, A. (2007). Synchronization control for physics-based collaborative virtual environments with shared haptics, Advanced Robotics 21(1): 1001–1029.
  • [13] Chiu, C.-S. and Chiang, T.-S. (2011). Observer-based exponential stabilization of Takagi–Sugeno fuzzy systems with state and input delays, Journal of Systems and Control Engineering 225(7): 993–1004.
  • [14] Duda, J. (2012). A Lyapunov functional for a system with a time-varying delay, International Journal of Applied Mathematics and Computer Science 22(2): 327–337, DOI: 10.2478/v10006-012-0024-7.
  • [15] El’sgol’ts, L.E. (1966). Introduction to the Theory of Differential Equations with Deviating Arguments, Holden-Day, San Francisco, CA.
  • [16] Fee (1998). Twin RotorMIMO System. Advanced Teaching Manual 1, 33-007-4M5.
  • [17] Gahinet, P., Nemirovski, A., Laub, A.J. and Chilali, M. (1995). LMI Control Toolbox, MathWorks, Natick, MA.
  • [18] Gassara, H., El-Hajjaji, A. and Chaabane, M. (2010). Delay-dependent H-infinite exponential stabilization of T–S fuzzy systems with interval time-varying delay, Proceeding of the 49th IEEE Conference on Decision and Control, Atlanta, GA, USA, pp. 4281–4286.
  • [19] Gassaraa, A., El Hajjajia, A., Kchaoub, M. and Chaabaneb, M. (2014). Observer based (q,v,r)-α-dissipative control for TS fuzzy descriptor systems with time delay, Journal of the Franklin Institute 351(1): 187–206.
  • [20] Gonzalez, T., Rivera, P. and Bernal, M. (2012). Nonlinear control for plants with partial information via Takagi–Sugeno models: An application on the twin rotor MIMO system, 2012 9th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), DF, M´exico, pp. 1–6.
  • [21] Gopalsamy, K. (1992). Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer, Norwell, MA.
  • [22] Gu, K., Kharotonov, V. and Chen, J. (2003). Stability of Time Delay Systems, Birkhauser, Basel.
  • [23] Hahn, W. (1967). Stability of Motion, Springer-Verlag, Berlin.
  • [24] Kabakov, I. (1946). Concerning the control process for the steam pleasure, Inzhenernii Sbornik 2(1): 27–76.
  • [25] Kang, Q. and Wang, W. (2010). Guaranteed cost control for T–S fuzzy systems with time-varying delays, Journal of Control Theory and Applications 8(4): 413–417.
  • [26] Kelly, F.P. (2001). Mathematical modelling of the internet, in B. Engquist and W. Schmid (Eds.), Mathematics Unlimited—2001 and Beyond, Vol. 1, Springer-Verlag, Berlin, pp. 685–702.
  • [27] Kharitonov, V. and Hinrichsen, D. (2004). Exponential estimates for time delay systems, Systems & Control Letters 53(1): 395–405.
  • [28] Krasovskii, N. (1956). On the application of the second method of Lyapunov for equations with time delays, Prikladnaya Matematika i Mekhanika 20(3): 315–327.
  • [29] La Salle, J. and Lefschetz, S. (1961). Stability by Lyapunov’s Direct Method: With Applications, Academic Press, London.
  • [30] Li, J., Li, J. and Xia, Z. (2011). Delay-dependent generalized H2 control for discrete T–S fuzzy large-scale stochastic systems with mixed delays, International Journal of Applied Mathematics and Computer Science 21(4): 585–603, DOI: 10.2478/v10006-011-0046-6.
  • [31] Lin, C., Wang, Q., Lee, T.H. and Chen, B. (2007). Observer-based h∞ control for T–S fuzzy systems with time delay: Delay-dependent design method, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 34(4): 1030–1038.
  • [32] Lin, C., Wang, Q., Lee, T.H. and He, Y. (1991). LMI Approach to Analysis and Control of Takagi–Sugeno Fuzzy Systems with Time-Delay, Prentice Hall, New York, NY.
  • [33] Liu, H., Shi, P., Karimi, H. and Chadli, M. (2014). Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay, International Journal of Systems Science 1(1): 1–12.
  • [34] Marquez Rubio, J.F., del Muro Cuéllar, B. and Sename, O. (2012). Control of delayed recycling systems with an unstable pole at forward path, American Control Conference (ACC), Montreal, Canada, pp. 5658–5663.
  • [35] Mondie, S. and Kharitonov, V. (2005). Exponential estimates for retarded time-delay systems: An LMI approach, IEEE Transactions on Automatic Control 50(2): 268–273.
  • [36] Murray, R.M. (Ed.) (2003). Control in an Information Rich World: Report of the Panel on Future Directions in Control, SIAM, Philadelphia, PA.
  • [37] Neimark, J.I. (1973). D-decomposition of spaces of quasi-polynomials, AmericanMathematical Society Translations 102(2): 95–131.
  • [38] Nejjari, F., Rotondo, D., Puig, V. and Innocenti, M. (2011). LPV modelling and control of a twin rotor MIMO system, 19th Mediterranean Conference on Control Automation (MED), 2011, Corfu, Greece, pp. 1082–1087.
  • [39] Niculescu, S.-I., Morărescu, C., Michiels, W. and Gu, K. (2007). Geometric ideas in the stability analysis of delay models in biosciences, in I. Queinnec et al. (Eds.), Biology and Control Theory: Current Challenges, Lecture Notes in Control and Information Sciences, Vol. 317, Springer Verlag, Berlin/Heidelberg, pp. 217–259.
  • [40] Oliveira, M. and Skelton, R. (2001). Stability tests for constrained linear systems, in S.Q.R. Moheimani (Ed.), Perspectives in Robust Control, Lecture Notes in Control and Information Sciences, Vol. 268, Springer-Verlag, Berlin, pp. 241–257.
  • [41] Pratap, B. and Purwar, S. (2010). Neural network observer for twin rotor MIMO system: An LMI based approach, 2010 International Conference on Modelling, Identification and Control (ICMIC), Okayama, Japan, pp. 539–544.
  • [42] Ramírez, A., Espinoza, E.S., García, L.R., Mondié, S., García, A. and Lozano, R. (2014). Stability analysis of a vision-based UAV controller, Journal of Intelligent and Robotic Systems 74(1): 69–84.
  • [43] Razumikhin, B. (1956). On stability of systems with a delay, Prikladnaya Matematika i Mekhanika 20(1): 500–512.
  • [44] Speich, E. and Rose, J. (2004). Medical Robotics, Prentice Hall, Marcel Dekker, New York, NY.
  • [45] Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control, IEEE Transactions on Systems Man and Cybernetics 15(1): 116–132.
  • [46] Tanaka, K. and Sugeno, M. (1990). Stability analysis of fuzzy systems using Lyapunov’s direct method, NAFIPS’90, Kanazawa, Japan, pp. 133–136.
  • [47] Tanaka, K. and Wang, H. (2001). Fuzzy Control Systems Design and Analysis. A Linear Matrix Inequality Approach, John Wiley & Sons, New York, NY.
  • [48] Taniguchi, T., Tanaka, K. and Wang, H. (2001). Model construction, rule reduction and robust compensation for generalized form of Takagi–Sugeno fuzzy systems, IEEE Transactions on Fuzzy Systems 9(2): 525–537.
  • [49] Tao, C., Taur, J.-S., Chang, Y.-H. and Chang, C.-W. (2010). A novel fuzzy-sliding and fuzzy-integral-sliding controller for the twin-rotor multi-input-multi-output system, IEEE Transactions on Fuzzy Systems 18(5): 893–905.
  • [50] Thuan, M.V., Phat, V.N. and Trinh, H. (2012). Observer-based controller design of time-delay systems with an interval time-varying delay, International Journal of AppliedMathematics and Computer Science 22(4): 921–927, DOI: 10.2478/v10006-012-0068-8.
  • [51] Tuan, H., Apkarian, P., Narikiyo, T. and Yamamoto, Y. (2001). Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Transactions on Fuzzy Systems 9(2): 324–332.
  • [52] Tzypkin, J. (1946). Stability of systems with delayed feedback, Automatic and Remote Control 7(2): 107–129.
  • [53] Wang, H., Tanaka, K. and Griffin, M. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Transactions on Fuzzy Systems 4(1): 14–23.
  • [54] Wang, Z., Ho, D. and Liu, X. (2004). A note on the robust stability of uncertain stochastic fuzzy systems with time-delays, IEEE Transactions on System, Man, and Cybernetics A 34(4): 570–576.
  • [55] Yu, L. and Chu, J. (1999). An LMI approach to guaranteed cost control of linear uncertain time-delay systems, Automatica 35(1): 1155–1159.
  • [56] Zhang, B., Lam, J., Xu, S. and Shu, Z. (2009). Robust stabilization of uncertain T–S fuzzy time-delay systems with exponential estimates, Fuzzy Sets and Systems 160(12): 1720–1737.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8eb835b9-a15f-4478-8d2b-02c15e5186b1
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