Exponential Stability Analysis for Switched Cellular Neural Networks with Time-varying Delays and Impulsive Effects
In this Letter, a class of impulsive switched cellular neural networks with time-varying delays is investigated. At the same time, parametric uncertainties assumed to be norm bounded are considered. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions guaranteeing exponential stability for all admissible parametric uncertainties are derived via constructing appropriate Lyapunov functional. One numerical example is provided to illustrate the validity of the main results obtained in this paper.
[1] L. Chua, L. Yang, Cellular neural networks: Theory, IEEE Trans. Circuits
Syst, 35 (1988) 1257-1272.
[2] Q. Wang, X. Liu, Exponential stability of impulsive cellular neural
networks with time delay via Lyapunov functionals, Applied Mathematics
and Computation, 194 (2007) 186-198.
[3] H. Wang, X. Liao, and C. Li, Existence and exponential stability of
periodic solution of BAM neural networks with impulse and time-varying
delay, Chaos, Solitons & Fractals, 33 (2007) 1028-1039.
[4] S. Mohamad, Exponential stability in Hopfield-type neural networks with
impulses, Chaos, Solitons & Fractals, 32 (2007) 456-467.
[5] Z. Huang, X. Luo, Q. Yang, Global asymptotic stability analysis of
bidirectional associative memory neural networks with distributed delays
and impulse, Chaos, Solitons & Fractals, 34 (2007) 878-885.
[6] Y. Li, W. Xing, and L. Lu, Existence and global exponential stability
of periodic solution of a class of neural networks with impulses, Chaos,
Solitons & Fractals, 27 (2006) 437-445.
[7] J. Mancilla-Aguilar, R. Garciaa, An extension of LaSalles invariance
principle for switched systems, Systems and Control Letters, 55 (2006)
376- 384.
[8] W. Feng, J. Zhang, Stability analysis and stabilization control of multivariable
switched stochastic systems, Automatica, 42 (2006) 169-176.
[9] N. ElFarra, P. Mhaskar, and P. Christofides, Output feedback control of
switched nonlinear systems using multiple Lyapunov functions,Systems
and Control Letters, 54 (2005) 1163-182.
[10] G. Hu, On stability of switched homogeneous nonlinear systems, J. Math.
Anal. Appl, 334 (2007) 414-430.
[11] M. Sen, Quadratic stability and stabilization of switched dynamic systems
with un-commensurate internal point delays, Applied Mathematics
and Computation, 185 (2007) 508-526.
[12] F. Cao, Neural Networks with Single Hidden Layer and the Best
Polynomial Approximation, ACTA MATHEMATICA SINICA, Chinese
Series, 50 (2007) 385-392.
[13] F. Cao, Y. Zhang, Interpolation and Approximation by Neural Networks
in Distance Space, ACTA MATHEMATICA SINICA, Chinese Series, ,51
(2008) 91-98.
[1] L. Chua, L. Yang, Cellular neural networks: Theory, IEEE Trans. Circuits
Syst, 35 (1988) 1257-1272.
[2] Q. Wang, X. Liu, Exponential stability of impulsive cellular neural
networks with time delay via Lyapunov functionals, Applied Mathematics
and Computation, 194 (2007) 186-198.
[3] H. Wang, X. Liao, and C. Li, Existence and exponential stability of
periodic solution of BAM neural networks with impulse and time-varying
delay, Chaos, Solitons & Fractals, 33 (2007) 1028-1039.
[4] S. Mohamad, Exponential stability in Hopfield-type neural networks with
impulses, Chaos, Solitons & Fractals, 32 (2007) 456-467.
[5] Z. Huang, X. Luo, Q. Yang, Global asymptotic stability analysis of
bidirectional associative memory neural networks with distributed delays
and impulse, Chaos, Solitons & Fractals, 34 (2007) 878-885.
[6] Y. Li, W. Xing, and L. Lu, Existence and global exponential stability
of periodic solution of a class of neural networks with impulses, Chaos,
Solitons & Fractals, 27 (2006) 437-445.
[7] J. Mancilla-Aguilar, R. Garciaa, An extension of LaSalles invariance
principle for switched systems, Systems and Control Letters, 55 (2006)
376- 384.
[8] W. Feng, J. Zhang, Stability analysis and stabilization control of multivariable
switched stochastic systems, Automatica, 42 (2006) 169-176.
[9] N. ElFarra, P. Mhaskar, and P. Christofides, Output feedback control of
switched nonlinear systems using multiple Lyapunov functions,Systems
and Control Letters, 54 (2005) 1163-182.
[10] G. Hu, On stability of switched homogeneous nonlinear systems, J. Math.
Anal. Appl, 334 (2007) 414-430.
[11] M. Sen, Quadratic stability and stabilization of switched dynamic systems
with un-commensurate internal point delays, Applied Mathematics
and Computation, 185 (2007) 508-526.
[12] F. Cao, Neural Networks with Single Hidden Layer and the Best
Polynomial Approximation, ACTA MATHEMATICA SINICA, Chinese
Series, 50 (2007) 385-392.
[13] F. Cao, Y. Zhang, Interpolation and Approximation by Neural Networks
in Distance Space, ACTA MATHEMATICA SINICA, Chinese Series, ,51
(2008) 91-98.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55506", author = "Zixin Liu and Fangwei Chen", title = "Exponential Stability Analysis for Switched Cellular Neural Networks with Time-varying Delays and Impulsive Effects", abstract = "In this Letter, a class of impulsive switched cellular neural networks with time-varying delays is investigated. At the same time, parametric uncertainties assumed to be norm bounded are considered. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions guaranteeing exponential stability for all admissible parametric uncertainties are derived via constructing appropriate Lyapunov functional. One numerical example is provided to illustrate the validity of the main results obtained in this paper.
", keywords = "Switched systems, exponential stability, cellular neural networks.", volume = "4", number = "8", pages = "1130-7", }
