AUTHORS: Wajaree Weera, Thongchai Botmart

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ABSTRACT: This paper is considered with the problem of robust absolute stability of neutral type Lur’e systems with mixed time-varying delays. By constructing an new augmented Lyapunov-Krasovskii functional and combining integral inequality with approach to estimate the derivative of the Lyapunov-Krasovskii functional, which estimated some integral terms byWirtinger’s inequality, a matrix-based quadratic convex technique is used to design an LMIbased sufficient conditions. New stability condition is much less conservative and more general than some existing results. New stability criteria is given in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

KEYWORDS: robust absolute stability, neutral type, Lur’e system, mixed time-varying delays, LMI approach

REFERENCES:

[1] I. Amri, D. Soudani and M. Benrejeb, Delay– dependent robust exponentially stability criteria for perturbed and uncertain neutral systems with time-varying delays, Stud. Inform. Contol., 19, 2010, pp. 135–144.

[2] T. Botmart, P. Niamsup and V. N. Phat, Delay–dependent exponential stabilization for uncertain linear systems with interval non– differentiable time-varying delays,Appl. Math. Comput., 217, 2011, pp. 8236–8247.

[3] J. Cao, G. Chen and P. Li, Synchronization for Coupled Neural Networks With Interval Delay A Novel Augmented Lyapunov-Krasovskii Functional Method, IEEE Trans. Neural Netw. Learn. Syst., 22, 2013, pp. 58–70.

[4] J. Cao, L. Li, Cluster synchronization in an array of hybrid coupled neural networks with delay, Neural Netw., 22, 2009, pp. 335–342.

[5] Y. Chen, W. Bi and W. Li,New delay–dependent absolute stability criteria for Lur’e systems with time–varying delay, Internat. J. Systems Sci. , 42, 2011, pp. 1105–1113.

[6] K. Gu, V. L. Kharitonov and J. Chen, Stability of time–delay system., Boston: Birkhauser; 2003.

[7] J. F. Gao, H. P. Pan and X. F. Ji, A new delay–dependent absolute stability criterion for Lurie systems with time–varying delay, IActa Automat. Sinica., 36, 2010, pp. 845–850.

[8] Q. L. Han, A. Xue, S. Liu and X. Yu, Robust absolute stability criteria for uncertain Lur’e systems of neutral type, Internat. J. Robust Nonlinear Control, 18, 2008, pp. 278–295.

[9] Q. L. Han, D. Yue, Absolute stability of Lure systems with time–varying delay, IIET Control Theory Appl., 1, 2007, pp. 854–859.

[10] H. K. Khalil, Nonlinear Systems, Prentice–Hall, Upper Saddle River, NJ, 1996.

[11] O. M. Kwon, J. H. Park, Exponential stability for time–delay systems with interval time– varying delays and nonlinear perturbations, J. Optim. Theory Appl., 13, 2008, pp. 277–293. WSEAS TRANSACTIONS on MATHEMATICS Wajaree Weera, Thongchai Botmart E-ISSN: 2224-2880 27 Volume 16, 2017

[12] O. M. Kwon, J. H. Park and S. M. Lee, On robust stability criterion for dynamic systems with time–varying delays and nonlinear perturbations, Appl. Math. Comput., 203, 2008, pp. 937–942.

[13] X. X. Liao, Absolute Stability of Nonlinear Control Systems, Science Press, Beijing, 1993.

[14] T. Li, W. Qian, T. Wang and S. Fei, Further results on delay–dependent absolute and robust stability for time–delay Lur’e system, Internat. J. Robust Nonlinear Control, 24, 2014, pp. 3300- 3316.

[15] X. Liu, J. Z. Wang and Z. S. Duan, New absolute stability criteria for time–delay Lure systems with sector–bounded nonlinearity, Internat. J. Robust Nonlinear Control, 20, 2010, pp. 659– 672.

[16] R. Lun, H. Wu and J. Bai, New delay–dependent robust stability criteria for uncertain neutral systems with mixed delays, J. Franklin Inst., 351, 2014, pp. 1386–1399.

[17] J. H. Park, Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations, Appl. Math. Comput., 161, 2005, pp. 413–421, 2005.

[18] V. M. Popov, Hyperstability of Control Systems, Springer, New York, 1973.

[19] F. Qiu, B. Cui and Y.Ji, Further results on robust stability of neutral system with mixed time–varying delays and nonlinear perturbations, Nonlinear Anal., 11, 2010, pp. 895–906.

[20] K. Ramakrishnan, G. Ray, An improved delay– dependent stability criterion for a class of Lure systems of neutral type, J. Dyn. Syst., 134, 2012, pp. 011008.

[21] A. Seuret, F. Gouaisbaut, Wirtinger–based integral inequality: Application to time–delay systems,” Automat., 49, 2013, pp. 2860–2866.

[22] Y. T. Wang, X. Zhang and Y. He. Chen, Improved delay–dependent robust stability criteria for a class of uncertain mixed neutral and Lure dynamical systems with interval time– varying delays and sector–bounded nonlinearity, J. Franklin Inst., 347, 2010, pp. 1623–1642.

[23] W. Weera, P. Niamsup, Robust Stability of a Class of Uncertain Lur’e Systems of Neutral Type, Abstr. Appl. Anal., 2012, 2012, pp. 1–18.

[24] K. Y. Yu, C. H. Lien, Stability criterion for uncertain neutral systems with interval time– varying delays, Chaos Solitons Fractals, 38, 2008, pp. 650–657.