Stability analysis for a class of switched nonlinear time-delay systems

Systems Science and Control Engineering

Volumn 2, Issue 1, 2014, Pages 80-89

  Kermani, M ^a   Sakly, A ^a  

^a UNIVERSITY OF MONASTIR   (Tunisia)

Author keywords

Arbitrary switching; Arrow matrix; Discrete time switched nonlinear time delay systems; Global asymptotic stability; Kotelyanski lemma; M matrix

Indexed keywords

ASYMPTOTIC STABILITY; DELAY CONTROL SYSTEMS; DIFFERENCE EQUATIONS; LYAPUNOV FUNCTIONS; TIME DELAY; TIMING CIRCUITS;

ARBITRARY SWITCHING; GLOBAL ASYMPTOTIC STABILITY; KOTELYANSKI LEMMA; M-MATRICES; NONLINEAR TIME DELAY SYSTEMS;

SYSTEM STABILITY;

EID: 84901046067     PISSN: None     EISSN: 21642583     Source Type: Journal    
DOI: 10.1080/21642583.2013.879543     Document Type: Article

References (48)

1. Arunkumar, A., Sakthivel, R., Mathiyalagan, K., & Marshal Anthoni, S. (2012). Robust stability criteria for discrete-time switched neural networks with various activation functions. Applied Mathematics and Computation, 218, 10803–10816.
2. Arunkumar, A., Sakthivel, R., Mathiyalagan, K., & Marshal Anthoni, S. (2013). State estimation for switched discrete-time stochastic BAM neural networks with time varying delay. Nonlinear Dynamics, 73, 1565–1585.
3. Benrejeb, M., & Borne, P. (1978). On an algebraic stability criterion for non-linear processes. Interpretation in the frequency domain. Proceedings of the measurement and control international symposium MECO’78, Eugenidis Foundation, Athens, Greece, pp. 678–682.
4. Benrejeb, M., Borne, P., & Laurent, F. (1982). Sur une application de la représentation en flèche à l’analyse des processus. RAIRO Automatique – Systems analysis and control, 16, 133–146.
5. Benrejeb, M., & Gasmi, M. (2001). On the use of an arrow form matrix for modelling and stability analysis of singularly perturbed nonlinear systems. System Analysis Modelling Simulation, 40, 509–525.
6. Benrejeb, M., Gasmi, M., & Borne, P. (2005). New stability conditions for TS fuzzy continuous nonlinear models. Nonlinear Dynamics System Theory, 5, 369–379.
7. Benrejeb, M., Soudani, D., Sakly, A., & Borne, P. (2006). New discrete Tanaka domain Sugeno Kang fuzzy systems characterization and stability domain. International Journal of Computers, Communications and Control, I, 9–19.
8. Borne, P. (1987). Nonlinear system stability: Vector norm approach. System and Control Encyclopedia, t.5, 3402–3406.
9. Borne, P., Gentina, J. C., & Laurent, F. (1972). Sur la stabilité des systèmes Échantillonnés non linéaires. Revue française d’automatique, informatique et de recherche opérationnelle, 2, 96–105.
10. Borne, P., Vanheeghe, P., & Duflos, E. (2007). Automatisation des processus dans l’espace d’état. Paris: Ed. Technip.
11. Branicky, M. S. (1998). Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, 43(4), 475–482.
12. Darouach, M., & Chadli, M. (2013). Admissibility and control of switched discrete-time singular systems. Systems Science and Control Engineering: An Open Access Journal, 1(1), 43–51.
13. Dong, Y., Liu, J., Mei, S., & Li, M. (2011). Stabilization for switched nonlinear time-delay systems. Nonlinear Analysis: Hybrid Systems, 5, 78–88.
14. Elmadssia, S., Saadaoui, K., & Benrejeb, M. (2011). New delay-dependent stability conditions for linear systems with delay. International conference on communications, computing and control applications (CCCA), Hammamet, Tunisia, pp. 1–6.
15. Elmadssia, S., Saadaoui, K., & Benrejeb, M. (2013). New delay-dependent stability conditions for linear systems with delay. Systems Science & Control Engineering, 1, 37–41.
16. Filali, R. L., Hammami, S., Benrejeb, M., & Borne, P. (2012). On synchronization, anti-synchronization and hybrid synchronization of 3D discrete generalized H12 non map. Nonlinear Dynamics System Theory, 12, 81–96.
17. Gantmacher, F. R. (1966). Théorie des matrices. T.1 et 2. Paris: Dunod.
18. Gao, H., & Chen, T. (2007). New results on stability of discrete-time systems with time-varying state delay. IEEE Transactions on Automatic Control, 52(2), 328–334.
19. Gao, H., Lam, J., & Wang, Z. (2007). Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis. Chaos, Solitons Fractals, 34(2), 394–404.
20. Hespanha, J. P., & Morse, A. S. (1999). Stability of switched systems with average dwell-time. 38th IEEE conference decision control, Arizona, USA, pp. 2655–2660.
21. Ishii, H., & Francis, B. A. (2002). Stabilizing a linear system by switching control with dwell time. IEEE Transactions on Automatic Control, 47, 1962–1973.
22. Jabbali, A., Kermani, M., & Sakly, A. (2013). A new stability analysis for discrete-time switched time-delay systems. Special Issue-international conference on control, engineering & information technology (CEIT’13), proceedings engineering & technology (PET), 1, 200–204.
23. Jianyin, F., & Kai, L. (2010). Stabilization of nonlinear systems under arbitrary switching law. Proceedings of the 30th Chinese control conference, Yantai, China, pp. 641–643.
24. Kermani, M., Sakly, A., & M’sahli, F. (2012). A new stability analysis and stabilization of discrete-time switched linear systems using vector norms approach. World Academy of Science, Engineering and Technology, 71, 1302–1307.
25. Kotelyanski, D. M. (1952). Some properties of matrices with positive elements. Matematicheskii Sbornik [in Russian], 31, 497–505.
26. Liberzon, D. (2003). Switching in systems and control. Boston, MA: Birkhäuser.
27. Liberzon, D., & Morse, A. S. (1999). Basic problems in stability and design of switched systems. IEEE Control Systems Magazine, 19, 57–70.
28. Lien, C. H., Yu, K. W., Chang, H. C., Chung, L. Y., & Chen, J. D. (2012). Switching signal design for exponential stability of discrete switched systems with interval time varying delay. Journal of the Franklin Institute, 349, 2182–2192.
29. Lien, C. H., Yu, K. W., Chung, Y. J., Chang, H. C., Chung, L. Y., & Chen, J. D. (2011). Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay. Nonlinear Analysis: Hybrid Systems, 5, 10–19.
30. Mahmoud, M. S. (2010). Switched time-delay systems. Boston, MA: Springer-Verlag.
31. Mathiyalagan, K., Sakthivel, R., Marshal, & Anthoni, S. (2012). New robust exponential stability results for discrete-time switched fuzzy neural networks with time delays. Computers and Mathematics with Applications, 64, 2926–2938.
32. Phat, V. N., & Ratchagit, K. (2011). Stability and stabilization of switched linear discrete-time systems with interval time-varying delay. Nonlinear Analysis: Hybrid Systems, 5, 605–612.
33. Pellanda, P., Apkarian, P., & Tuan, H. (2002). Missile autopilot design via a multi-channel LFT/LPV control method. International Journal of Robust and Nonlinear Control, 12(1), 1–20.
34. Robert, F. (1966). Recherche d’une M-matrice parmi les mino-rantes d’un opérateur liéaire. Numerische Mathematik, 9, 188–199.
35. Sfaihi, B., & Benrejeb, M. (2013). On stability analysis of nonlinear discrete singularly perturbed T-S fuzzy models. International Journal of Dynamics and Control, 1, 20–31.
36. Shim, H., Noh, D. J., & Seo, J. H. (2001). Common Lyapunov function for exponentially stable nonlinear systems. Journal of Korean Institute of Electrical Engineers, 11, 108–111.
37. Sun, X. M., Wang, W., Liu, G. P., & Zhao, J. (2008). Stability analysis for linear switched systems with time-varying delay. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 38, 528–533.
38. Sun, Z., & Ge, S. S. (2011). Stability theory of switched dynamical systems. London: Springer.
39. Tse, C. K., & Bernardo, M. Di., (2002). Complex behavior in switching power converters. Proceedings of the IEEE, 90(5), 768–781.
40. Vu, L., & Liberzon, D. (2005). Common Lyapunov functions for families of commuting nonlinear systems. Systems and Control Letters, 54, 405–416.
41. Wu, Z., Shi, P., Su, H., & Chu, J. (2011). Delay-dependent stability analysis for switched neural networks with time-varying delay. IEEE Transactions on Systems, Man, and Cybernetics, PartB,41(6), 1522–1530.
42. Xu, S. (2002). Robust H1 filtering for a class of discrete-time uncertain nonlinear systems with state delay. IEEE Transactions on Circuits and Systems (I), 49, 1853–1859.
43. Zhai, G., Hu, B., Yasuda, K., & Michel, A. N. (2000). Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach. American control conference, Chicago, USA, vol. 1, pp. 200–204.
44. Zhang, H., Liu, Z., & Huang, G. (2010). Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via sc technique. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 40(6), 1480–1491.
45. Zhang, L., Shi, P., & Basin, M. (2008). Robust stability and stabilization of uncertain switched linear discrete time-delay systems. IET Proceedings Control Theory and Applications, 2, 606–614.
46. Zhang, L. X., & Gao, H. J. (2010). Asynchronously switched control of switched linear systems with average dwell time. Automatica, 46(5), 953–958.
47. Zhang, W., Abate, A., Hu, J., & Vitus, M. P. (2009). Exponential stabilization of discrete-time switched linear systems. Automatica, 45, 2526–2536.
48. Zhang, W. A., & Yu, L. (2009). Stability analysis for discrete-time switched time-delay systems. Automatica, 45, 2265–2271.