Abstract
In this paper, we consider the problem of delay-dependent stability of a class of discrete-time Lur’e systems with interval time-delay and sector-bounded nonlinearity using Lyapunov approach. By exploiting a candidate Lyapunov functional, and using slack matrix variables in the delay-dependent stability analysis, less conservative absolute and robust stability criteria are developed respectively for nominal and uncertain discrete-time Lur’e systems in terms of linear matrix inequalities (LMIs). For deriving robust stability conditions, time-varying norm-bounded uncertainties are considered in the system matrices. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed results.
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References
Popov, V.M.: Hyperstability of Control Systems. Springer, New York (1973)
Khalil, H.K.: Nonlinear Systems. Prentice-Hall, Upper Saddle River (1996)
Liao, X.X.: Absolute Stability of Nonlinear Control Systems. Science Press, Beijing (1993)
Yalcin, M.E., Suykens, J.A.K., Vandewalle, J.: Master-slave synchronization of Lur’e systems with time-delay. Internat. J. Bifurcation Chaos 11, 1707–1722 (2001)
Liao, X., Chen, G.: Chaos synchronization of general Lur’e systems via time-delay feedback control. Internat. J. Bifurcation Chaos 13, 207–213 (2003)
Cao, J., Li, H.X., Ho, D.W.C.: Synchronization criteria of Lur’e system with time-delay feedback control. Chaos Solitons Fractals 23, 1285–1298 (2005)
He, Y., Wu, M.: Absolute stability for multiple delay general Lur’e control systems with multiple nonlinearities. J. Comput. Appl. Math. 159, 241–248 (2003)
He, Y., Wu, M., She, J.H., Liu, G.P.: Robust stability for delay Lur’e systems with multiple nonlinearities. J. Comput. Appl. Math. 176, 371–380 (2005)
Han, Q.L., Yue, D.: Absolute stability of Lur’e systems with time-varying delay. IET Control Theory Appl. 1, 854–859 (2007)
Ramakrishnan, K., Ray, G.: Delay-range-dependent stability criteria for Lur’e system with interval time-varying delay. In: Proceedings of 49th IEEE Conf. Decision Cont., pp. 170–175 (2010)
Ramakrishnan, K., Ray, G.: Improved delay-range-dependent robust stability criteria for a class of Lur’e systems with sector-bounded nonlinearity. J. Franklin Inst. 348, 1769–1786 (2011)
Hao, F.: Absolute stability of uncertain discrete Lur’e systems and maximum admissible perturbed bounds. J. Franklin Inst. 347, 1511–1525 (2010)
Lee, S.M., Park, J.H.: Robust stabilization of discrete-time nonlinear Lur’e systems with sector and slope restricted nonlinearities. Appl. Math. Comput. 200, 429–436 (2008)
Huang, H., Feng, G.: Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay. IET Cont. Theory Appl. 4, 2152–2159 (2010)
Yang, C., Zhang, Q., Zhou, L.: Strongly absolute stability problem of descriptor systems: Circle criterion. J. Franklin Inst. 345, 437–451 (2008)
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Krishnan, R., Ray, G. (2012). Delay-Dependent Stability Criteria for Uncertain Discrete-Time Lur’e Systems with Sector-Bounded Nonlinearity. In: Balasubramaniam, P., Uthayakumar, R. (eds) Mathematical Modelling and Scientific Computation. ICMMSC 2012. Communications in Computer and Information Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28926-2_22
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DOI: https://doi.org/10.1007/978-3-642-28926-2_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28925-5
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