Abstract
Stochastic phenomena are common in many branches of science and engineering, and stochastic perturbations can be a source of instability in systems. This has made stochastic systems an interesting topic of research; and stochastic modeling has become an important tool in science and engineering. Increasing attention is now being paid to the stability, stabilization, and H∞ control of stochastic time-delay systems [1–6].
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References
S. Xu and T. Chen. Robust H∞ control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control, 47(12): 2089–2094, 2002.
C. Y. Lu, J. S. H. Tsai, G. J. Jong, and T. J. Su. An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays. IEEE Transactions on Automatic Control, 48(2): 286–289, 2003.
S. Xu and T. Chen. Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers. Systems & Control Letters, 51(3–4): 171–183, 2004.
W. H. Chen, Z. H. Guan, and X. M. Lu. Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach. Systems & Control Letters, 54(6): 547–555, 2005.
Y. S. Fu, Z. H. Tian, and S. J. Shi. Output feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Transactions on Automatic Control, 50(6): 847–851, 2005.
Z. H. Guan, W. H. Chen, and J. X. Xu. Delay-dependent stability and stabilizability of uncertain jump bilinear stochastic systems with mode-dependent time-delays. International Journal of Systems Science, 36(5): 275–285, 2005.
H. C. Yan, X. H. Huang, H. Zhang, and M. Wang. Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay. Chaos, Solitons & Fractals, 40(4): 1668–1679, 2009.
D. Yue and Q. L. Han. Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity and Markovian switching. IEEE Transactions on Automatic Control, 50(2): 217–222, 2005.
Y. Zhang, Y. He, and M. Wu. Improved delay-dependent robust stability for uncertain stochastic systems with time-varying delay. Proceeding of the 27th Chinese Control Conference, Kunming, China, 764–768, 2008.
Y. He, Y. Zhang, M. Wu, and J. H. She. Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay. International Journal of Robust and Nonlinear Control, in press, 2008.
X. R. Mao and L. Shaikhet. Delay-dependent stability criteria for stochastic differential delay equations with Markovian switching. Stability and Control: Theory and Applications, 3(2): 87–101, 2000.
Z. Shu, J. Lam, and S. Y. Xu. Robust stabilization of Markovian delay systems with delay-dependent exponential estimates. Automatica, 42(11): 2001–2008, 2006.
S. Xu and X. R. Mao. Delay-dependent H∞ control and filtering for uncertain Markovian jump system with time-varying delay. IEEE Transactions on Circuits and systems I, 54(9): 2070–2077, 2007.
H. J. Kushner. Stochastic Stability and Control. New York: Academic Press, 1967.
A. V. Skorohod. Asymptotic Methods in the Theory of Stochastic Differential Equations. Providence, RI: American Mathematical Society, 1989.
X. R. Mao. Robustness of exponential stability of stochastic differential delay equation. IEEE Transactions on Automatic Control, 41(3): 442–447, 1996.
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(2010). Stability of Stochastic Systems with Time-Varying Delay. In: Stability Analysis and Robust Control of Time-Delay Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03037-6_13
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DOI: https://doi.org/10.1007/978-3-642-03037-6_13
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