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Global rational stabilization of a class of nonlinear time-delay systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy.
Rocznik
Strony
259--278
Opis fizyczny
Bibliogr. 29 poz., wykr., wzory
Twórcy
autor
  • Gafsa University, Faculty of Sciences of Gafsa, Department of Mathematics, Zarroug Gafsa 2112 Tunisia
  • Gafsa University, Faculty of Sciences of Gafsa, Department of Mathematics, Zarroug Gafsa 2112 Tunisia
Bibliografia
  • [1] J. Anthonis, A. Seuret, J. P. Richard, and H. Ramon: Design of a pressure control system with band time delay. IEEE Transactions on Control Systems Technology, 15(6) (2007), 1103–1111.
  • [2] J. Baillieul and P. J. Antsaklis: Control and communication challenges in networked real-time systems. Proc. IEEE, 95(1) (2007), 9–28.
  • [3] A. Benabdallah: A separation principle for the stabilization of a class of time delay nonlinear systems. Kybernetika, 51(1) (2015), 99–111.
  • [4] A. Benabdallah and N. Echi: Global exponential stabilisation of a class of nonlinear time-delay systems. Int. J. of Systems Science, 47(16) (2016), 3857–3863.
  • [5] B. Ben Hamed: On the robust practical global stability of nonlinear time-varying systems. Mediterranean J. of Mathematics, 10(3) (2013), 1591–1608.
  • [6] N. Echi and A. Benabdallah: Delay-dependent stabilization of a class of time-delay nonlinear systems: LMI approach. Advances in Difference Equations, 271(1) (2017).
  • [7] M. Farza, A. Sboui, E. Cherrier, and M. M’Saad: High-gain observer for a class of time-delay nonlinear systems. Int. J. of Control, 83(2) (2010), 273–280.
  • [8] J. P. Gauthier, H. Hammouri, and S. Othman: A Simple Observer for Nonlinear Systems – Application to Bioreactors. IEEE Transactions on Automatic Control, 37(6) (1992), 875–880.
  • [9] A. Germani, C. Manes, and P. Pepe: Local asymptotic stability for nonlinear state feedback delay systems. Kybernetika, 36(1) (2000), 31–42.
  • [10] A. Germani, C. Manes, and P. Pepe: An asymptotic state observer for a class of nonlinear delay systems. Kybernetika, 37(4) (2001), 459–478.
  • [11] M. Ghanes, J. De Leon, and J. Barbot: Observer design for nonlinear systems under unknown time-varying delays. IEEE Transactions on Automatic Control, 58(6) (2013), 1529–1534.
  • [12] S. Ibrir: Observer-based control of a class of time-delay nonlinear systems having triangular structure. Automatica, 47(2) (2011), 388–394.
  • [13] C. Jammazi and M. Zaghdoudi: On the rational stability of autonomous dynamical systems. Applications to control chained systems. Applied Mathematics and Computation, 219(20) (2013), 10158–10171.
  • [14] W. Hahn: Theory and Application of Liapunov’s Direct Method. Englewood Cliffs NJ, 1963.
  • [15] H. Hammouri and M. Farza: Nonlinear Observers for Locally Uniformly Observable Systems. ESAIM Journal on Control, Optimisation and Calculus of Variations, 9(9) (2003), 353–370.
  • [16] X. Li and C. D. Souza: Output feedback stabilization of linear time-delay systems. Stability and control of time-delay systems, Lecture Notes in Control and Information Sciences, 228 (1998), 241–258.
  • [17] C. Lili, Z. Ying, and Z. Xian: Guaranteed cost control for uncertain genetic regulatory networks with interval time-varying delays. Neurocomputing, 131 (2014), 105–112.
  • [18] Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee: Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. of Control, 74(14) (2001), 1447–1455.
  • [19] H. Mounier and J. Rudolph: Flatness Based Control of Nonlinear Delay Systems: A Chemical Reactor Example. Int. J. of Control, 71(5) (1998), 871–890.
  • [20] K. Natori and K. Ohnishi: Adesign method of communication disturbance observer for time-delay compensation, taking the dynamic property of network disturbance into account. IEEE Transaction on Industrial Electronics, 55(5) (2008), 2152–2168.
  • [21] P. Pepe and I. Karafyllis: Converse Lyapunov-Krasovskii theorems for systems described by neutral functional differential equations in Hales form. Int. J. of Control, 86(2) (2013), 232–243.
  • [22] V. N. Phat, Y. Khongtham, and K. Ratchagit: LMI approach to exponential stability of linear systems with interval time-varying delays. Linear Algebra and its Applications, 436(1) (2012), 243–251.
  • [23] G. Rajchakit, R. Saravanakumar, K. A. Choon, and R. K. Hamid: Improved exponential convergence result for generalized neural networks including interval time-varying delayed signals. Neural Networks, 86 (2017), 10-17.
  • [24] S. Ramasamy, M. S. Ali, C. K. Ahn, H. R. Karimi, and P. Shi: Stability of Markovian jump generalized neural networks with interval time-varying delays. IEEE Transactions on Neural Networks and Learning Systems, 8(28) (2016), 1840–1850.
  • [25] S. Ramasamy, G. Rajchakit, C. K. Ahn, and H. R. Karimi: Exponential stability, passivity, and dissipativity analysis of generalized neural networks with mixed time-varying delays. IEEE Transactions on Systems, Man and Cybernetics, 49(2) (2017), 395–405.
  • [26] Y. J. Sun: Global stabilization of uncertain systems with time-varying delays via dynamic observer-based output feedback. Linear Algebra and its Applications, 353(3) (2002), 91–105.
  • [27] M. V. Thuan, V. N. Phat, and H. Trinh: Trinh Observer-based controller design of time-delay systems with an interval time-varying delay. Int. J. of Applied Mathematics and Computer Science, 22(4) (2012), 921–927.
  • [28] J. Tsinias: A theorem on global stabilization of nonlinear systems by linear feedback. Systems Control Lettre, 17(5) (1991), 357–362.
  • [29] M. Zaghdoudi and C. Jammazi: On the rational stabilizability of nonlinear systems by optimal feedback control: The bilinear case. IEEE-3 rd Int. Conf. on Control Dicision and Information Technologie, 6(1) (2016), 466–471.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d9a448d2-5f48-47b0-b05c-369d568c10c5
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