References
- H. C. Chang and M. Aluko, Multi-scale analysis of exotic dynamics in surface catalyzed reactions-I, Chemical Engineering Science 39 (1984), 37-50. https://doi.org/10.1016/0009-2509(84)80128-1
- J. H. Chow, Time Scale Modelling of Dynamic Networks, Springer-Verlag, New York, 1982.
- P. D. Christofides and P. Dsoutidis, Feedback control of two-time-scale nonlinear systems, Internat. J. Control 63 (1996), no. 5, 965-994. https://doi.org/10.1080/00207179608921879
- J. H. Cruz and P. Z. Taboas, Periodic solutions and stability for a singularly perturbed linear delay differential equation, Nonlinear Anal. 67 (2007), 1657-1667. https://doi.org/10.1016/j.na.2006.08.004
- D. Da and M. Corless, Exponential stability of a class of nonlinear singularly perturbed systems with marginally sable boundary layer systems, In Proceedings of the American Control Conference, 3101-3106, San Francisco, CA, 1993.
- M. El-Ansary, Stochastic feedback design for a class of nonlinear singularly perturbed systems, Internat. J. Systems Sci. 22 (1991), no. 10, 2013-2023. https://doi.org/10.1080/00207729108910767
- M. El-Ansary and H. K. Khalil, On the interplay of singular perturbations and wide-band stochastic fluctuations, SIAM J. Control Optim. 24 (1986), no. 1, 83-94. https://doi.org/10.1137/0324004
- E. Fridman, Effects of small delays on stability of singularly perturbed systems, Automatica J. IFAC 38 (2002), no. 5, 897-902. https://doi.org/10.1016/S0005-1098(01)00265-5
- V. B. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 1992.
- X. Z. Liu, X. M. Shen, and Y. Zhang, Exponential stability of singularly perturbed systems with time delay, Appl. Anal. 82 (2003), no. 2, 117-130. https://doi.org/10.1080/0003681031000063775
- X. R. Mao, Razumikhin-type theorems on exponential stability of stochastic functional-differential equations, Stochastic Process. Appl. 65 (1996), no. 2, 233-250. https://doi.org/10.1016/S0304-4149(96)00109-3
- X. R. Mao, Stochastic Differential Equations and Applications, Horwood Publication, Chichester, 1997.
- X. R. Mao, Stochastic versions of the LaSalle theorem, J. Differential Equations 153 (1999), no. 1, 175-195. https://doi.org/10.1006/jdeq.1998.3552
- S.-E. A. Mohammed, Stochastic Functional Differential Equations, Longman Scientific and Technical, 1986.
- J. J. Monge and C. Georgakis, The effect of operating variables on the dynamics of catalytic cracking processes, Chemical Engineering Communications 60 (1987), 1-15. https://doi.org/10.1080/00986448708912007
- N. Prljaca and Z. Gajic, A method for optimal control and filtering of multitime-scale linear singularly-perturbed stochastic systems, Automatica J. IFAC 44 (2008), no. 8, 2149-2156. https://doi.org/10.1016/j.automatica.2007.12.001
- L. Socha, Exponential stability of singularly perturbed stochastic systems, IEEE Trans. Automat. Contr. 45 (2000), no. 3, 576-580. https://doi.org/10.1109/9.847748
- H. J. Tian, The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag, J. Math. Anal. Appl. 270 (2002), no. 1, 143-149. https://doi.org/10.1016/S0022-247X(02)00056-2
-
H. J. Tian, Dissipativity and exponential stability of
${\theta}$ -method for singularly perturbed delay differential equations with a bounded lag, J. Comput. Math. 21 (2003), no. 6, 715-726. -
H. J. Tian, Numerical and analytic dissipativity of the
${\theta}$ -method for delay differential equations with a bounded variable lag, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 14 (2004), no. 5, 1839-1845. https://doi.org/10.1142/S0218127404010096 - L. G. Xu, Exponential p-stability of singularly perturbed impulsive stochastic delay differential systems, Int. J. Control. Autom. 9 (2011), no. 5, 966-972. https://doi.org/10.1007/s12555-011-0518-3
- D. Y. Xu, Z. G. Yang, and Y. M. Huang, Existence-uniqueness and continuation theorems for stochastic functional differential equations, J. Differential Equations 245 (2008), no. 6, 1681-1703. https://doi.org/10.1016/j.jde.2008.03.029
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