This paper mainly
tends to utilize Razumikhin-type theorems to investigate p-th moment stability
for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik-
hin methods, some sufficient conditions are derived to check the stability of stochastic
switching nonlinear systems with delay. One numerical example is provided to
demonstrate the effectiveness of the results.
References
[1]
Hale, J.K. and Lunel, S.M.V. (1993) Introduction to Functional Differential Equations. Springer-Verlag?, Berlin.
http://dx.doi.org/10.1007/978-1-4612-4342-7
[2]
Feng, W., Tian, J. and Zhao, P. (2011) Stability Analysis of Switched Stochastic Systems. Automatica, 47, 148-157.
http://dx.doi.org/10.1016/j.automatica.2010.10.023
[3]
Liu, J., Liu, X. and Xie, W. (2009) Exponential Stability of Switched Sto-chastic Delay Systems with Non-Linear Uncertainties. International Journal of Systems Science, 40, 637-648. http://dx.doi.org/10.1080/00207720902755770
[4]
Kolmanovskii, V.B. and Nosov, V.R. (1986) Stability of Functional Differential Equations. Academic Press, INC, New York.
[5]
Razumikhin, B.S. (1956) On the Stability of Systems with Delay. Prikl. Mat. Mekh, 20, 500-512.
[6]
Razumikhin, B.S. (1960) Application of Lyapunov’s Method to Problems in the Stability of Systems with a Delay. Automat, i Telemekh, 21, 740-749.
[7]
Mao, X. (1996) Razumikhin-Type Theorems on Exponential Stability of Stochastic Functional Differential Equations. Stochastic Processes and their Applications, 65, 233-250. http://dx.doi.org/10.1016/S0304-4149(96)00109-3
[8]
Mao, X. (1997) Razumikhin-type Theorems on Exponential Stability of Neutral Stochastic Functional Differential Equations. SIAM: SIAM Journal on Mathematical Analysis, 28, 389-401. http://dx.doi.org/10.1137/S0036141095290835
[9]
Mao, X., Lam, J. and Xu, S. (2006) Razumikhin Method and Exponential Sta-bility of Hybrid Stochastic Delay Interval Systems. Journal of Mathematical Analysis and Applications, 314, 45-66. http://dx.doi.org/10.1016/j.jmaa.2005.03.056
[10]
Wu, X., Zhang, W. and Tang, Y. (2013) pth Moment Stability of Impulsive Sto-chastic Delay Differential Systems with Markovian Switching. Communications in Nonlinear Science and Numerical Simulation, 18, 1870-1879.
http://dx.doi.org/10.1016/j.cnsns.2012.12.001
[11]
Hu, S., Huang, C. and Wu, F. (2008) Stochastic Differential Equations. Science Press, Beijing.
[12]
Wu, F. and Hu, S. (2012) Razumikhin-Type Theorems on General Decay Stability and Robustness for Stochastic Func- tional Differential Equations. International Journal of Robust and Nonlinear Control, 22, 763-777.
http://dx.doi.org/10.1002/rnc.1726
[13]
Chatterjee, D. and Liberzon, D. (2006) Stability Analysis of Deterministic and Stochastic Switched Systems via a Comparison Principle and Multiple Lyapunov Functions. SIAM Journal on Control and Optimization, 45, 174-206.
http://dx.doi.org/10.1137/040619429
