This paper presents a new nonlinear integral-type sliding surface for synchronizing two different chaotic systems with parametric uncertainty. On the basis of Lyapunov theorem and average dwelling time method, we obtain the control gains of controllers which are derived to achieve chaos synchronization. In order to reduce the gains, the error system is modeled as a switching system. We obtain the sufficient condition drawn for the robust stability of the error dynamics by stability analysis. Then we apply it to guide the design of the controllers. Finally, numerical examples are used to show the robustness and effectiveness of the proposed control strategy.<\/p>\r\n","references":"[1]\tL. M. Pecora, T. L. Carroll,. Synchronization in chaotic systems, Phys Rev Lett, Vol. 64, pp. 821-824, 1990.\r\n[2]\tH. Zhang, X.K. Ma, W.Z. Liu, Synchronization of chaotic systems with parametric uncertainty using active sliding mode control, Chaos Solit Fract, Vol. 21, pp. 1249-1257, 2004.\r\n[3]\tN. Cai, Y. Jing, S. Zhang, Modified projective synchronization of chaotic systems with disturbances via active sliding mode control, Commun Nonlinear Sci Numer Simulat, Vol. 15, pp. 1613-1620, 2010. \r\n[4]\tY. Meisam, R.N. Abolfazl, G. Reza, Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control, ISA Transactions, Vol. 50, pp. 262-267, 2011.\r\n[5]\tE. Ott, C. Grebogi, J. A. Yorke, Controlling Chaos, Phys. Rev. Lett.64, Vol.64, pp. 1196-1199, 1990.\r\n[6]\tM. Chen, Z. Han. Controlling and synchronizing chaotic Genesio system via nonlinear feedback control. Chaos, Solitons & Fractals Vol. 17, No. 4, pp.709-716, 2003.\r\n[7]\tV. Sundarapandian, Sliding mode controller design for the global chaos synchronization of hyperchaotic Xu systems. International Journal on Cybernetics & Informatics, Vol.1 No.2, pp. 23-33, 2012.\r\n[8]\tY. Gao, B. Sun, G. Lu, Modified function projective lag synchronization of chaotic systems with disturbance estimations, Applied Mathematical Modelling, Vol. 37, pp. 4993-5000, 2013.\r\n[9]\tJ. H. Park, O. M. Kwon, A novel criterion for delayed feedback control of time-delay chaotic systems, Chaos, Solitons & Fractals, Vol. 23, No. 2, pp.495-501, 2005.\r\n[10]\tQ. L. Han, New delay-dependent synchronization criteria for lur\u2019s systems using time delay feedback control, Phys. Lett. A, Vol. 360, pp. 563-569, 2007.\r\n[11]\tM. M. Polycarpou, Stable adaptive neural control scheme for nonlinear systems. IEEE Transactions on Automatic Control, Vol.41, No. 3, pp.447-451, 1996.\r\n[12]\tC. Cao, N. Hovakimyan. Design and analysis of a novel L1 adaptive control architecture with guaranteed transient performance. IEEE Transactions on Automatic Control, Vol.53, No. 2, pp 332-339, 2008.\r\n[13]\tL. Zhao, L.S. Shieh, G. N.P. Chen , Coleman N. P., Simplex sliding mode control for nonlinear uncertain systems via chaos optimization, Chaos, Solitons & Fractals, Vol. 23, pp,747-755, 2005.\r\n[14]\tQ. Hu, C. Du, L. Xie, Y. Wang, Discrete-time sliding mode control with time-varying surface for hard disk drives, IEEE Trans. Control System. Technology, Vol. 17, No. 1, pp. 175-183, 2009.\r\n[15]\tK. Y. Nikhil, R.K. Singh, Discrete-time nonlinear sliding mode controller, International Journal of Engineering, Science and Technology, Vol. 3, No.3, pp. 94-100, 2011.\r\n[16]\tZ. Wang, X. Shi, Lag synchronization of two identical Hindmarsh-Rose neuron systems with mismatched parameters and external disturbance via s single sliding mode controller, Applied Mathematics and Computation, Vol. 218, pp. 10914-10921, 2012.\r\n[17]\tY. Gao, B. Sun, G. Lu, Passivity-based integral sliding-mode control of uncertain singularly perturbed systems, IEEE Trans. On Circuits and Systems, Vol. 58, No. 6, pp. 386-390, 2011.\r\n[18]\tY. Gao, B. Sun, G. Lu, Passivity Analysis of Uncertain singularly perturbed systems, IEEE Trans. On Circuits and Systems, Vol. 57, No. 6, pp. 486-490, 2010.\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 85, 2014"}