Abstract
This paper considers the problem of delay-dependent stability of the systems with nonlinearity, uncertainty and time-varying delays. The uncertainty is assumed to be of norm-bounded form. By constructing Lyapunov-Krasovskii functional and introducing appropriate free-weighting matrices, the sufficient delay-dependent condition is derived for the asymptotic stability of the system. The proposed result is formulated in terms of linear matrix inequality, which can be efficiently solved by standard convex optimization algorithms.
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References
Xu, S., Chen, T.: Robust H ∞  control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control 47(12), 2089–2094 (2002)
Liao, X., Mao, X.: Exponential stability of stochastic delay interval systems. Systems & Control Letters 40, 171–181 (2000)
Xu, S., Shi, P., Chu, Y., Zou, Y.: Robust stochastic stabilization and H ∞  control of uncertain neutral stochastic time-delay systems. Journal of Mathematical Analysis and Applications 314, 1–6 (2006)
Huang, L., Deng, F.: Robust exponential stabilization of stochastic large-scale delay systems. In: Proceedings of 2007 IEEE international conference on control and automation, pp. 107–112 (2007)
Yue, D., Han, Q.L.: Delay-dependent exponential stability of stochastic systems with time-varying, nonlinearity and Markovian switching. IEEE Transactions on Automatic Control 50, 217–222 (2005)
Lu, H.Q., Zhou, W.N.: Delay-dependent robust H ∞  control for uncertain stochastic systems. Control and Decision 24(1), 76–80 (2009)
Huang, L.R., Mao, X.: Robust delayed-state-feedback stabilization of uncertain stochastic systems. Automatic 45, 1332–1339 (2009)
Yue, D., Fang, J., Won, S.: Delay-dependent robust stability of stochastic uncertain systems with time delay and markovian jump parameters. Circuits Syst. Signal Processing 22, 351–365 (2003)
Chen, W.H., Guan, Z.H., Lu, X.M.: Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach. Systems & Control Letters 54, 547–555 (2005)
Wei, G.L., Wang, Z.D., Shu, H.S.: Nonlinear H ∞  control of stochastic time-delay systems with Markovian switching. Chao, Solitons and Fractals 35, 442–451 (2008)
Gao, H.J., Lam, J., Wang, C.H.: Robust energy-to-peak filter design for stochastic time-delay systems. Systems & Control Letters 55, 101–111 (2006)
Xu, S.Y., Lam, J.: Exponential H ∞  filter design for uncertain Takagi-Sugeno fuzzy systems with time delay. Artificial Intelligence 17, 645–659 (2004)
Chen, Y., Xue, A.K., Wang, J.H.: Delay-dependent passive control of stochastic delay systems. Acta Automatica Sinica 35(3), 324–327 (2009)
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Wang, C. (2010). Delay-Dependent Stability of Nonlinear Uncertain Stochastic Systems with Time-Varying Delays. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13278-0_86
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DOI: https://doi.org/10.1007/978-3-642-13278-0_86
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13277-3
Online ISBN: 978-3-642-13278-0
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