Abstract
This article formulates and studies the stability of a kind of Hybrid Systems with time-delay. This system is assumed to be autonomous and the state delay is time-varying. Using the Lyapunov functional approach combined with linear matrix inequality technique, neither restriction on the derivative of time-delay function nor bound restriction on nonlinear switched systems with time-varying delays is required to analyze the exponential stability of this kind of nonlinear switched systems with time-varying delays. Some delay-dependent exponential stability conditions are derived by the stability theory. A numerical example is given for illustration and interpretation of the theoretical results.
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References
Bertsekas, D.: Note on the design of linear systems with piecewise constant feedback gains. IEEE Trans. Automat. Control 15, 262–263 (1970)
Molchanov, A.P., Pyatnitskiy, Y.S.: Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Syst. Contr. Lett. 13, 59–64 (1989)
Nair, G.N., Evans, R.J.: Exponential stabilisability of finite-dimensional linear systems with limited data rates. Automatica 39, 347–535 (2003)
Liberzon, D.: Switching in Systems and Control. Birkhauser, Boston (2003)
Liao, X., Wong, K.W.: Global exponential stability of hybrid bidirectional associative memory neural networks with discrete delay. Phys. Rev. E, Stat. Phys., Plasmas Fluids Relat Interdiscip Top 67, 042, 90 (2003)
Yuan, K., Cao, J., Li, H.X.: Robust stability of switched Cohen–Grossberg neural networks with mixed time-varying delays. IEEE Trans., Syst., Man Cybern. B, Cybern. 36, 1356–1363 (2003)
Huang, H., Qu, Y., Li, H.-X.: Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty. Phys. Lett. A 345, 345–354 (2005)
Sun, Z., Ge, S.: Switched Linear Systems Control and Design. Springer, London (2005)
Branicky, M.S., Borkar, V.S., Mitter, S.K.: A unified framework for hybrid control: Model and optimal control theory. IEEE Trans., Autom., Control 43, 31–45 (1998)
Li, X., Soh, Y., Wen, C.: Switched and Impulsive Systems, Analysis, Design and Applications. Springer, Berlin (2005)
Guan, Z.-H., Hill, D.J., Shen, X.: On hybrid impulsive and switching systems and application to nonlinear control. IEEE Trans., Autom. Control 50, 1058–1062 (2005)
Li, C., Feng, G., Huang, T.: On Hybrid Impulsive and Switching Neural Networks. IEEE Trans. on Sys., Man, and Cybernetics-part B 38, 1549–1560 (2008)
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Pu, Xc., Zhao, Hq. (2012). Stability of a Kind of Hybrid Systems with Time-Delay. In: Jin, D., Lin, S. (eds) Advances in Electronic Engineering, Communication and Management Vol.1. Lecture Notes in Electrical Engineering, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27287-5_26
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DOI: https://doi.org/10.1007/978-3-642-27287-5_26
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Online ISBN: 978-3-642-27287-5
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