On Stability for Hybrid System under Stochastic Perturbations
Main Article Content
Abstract
The aim of this paper is to find out suitable conditions for almost surely exponential
stability of communication protocols, considered for nonlinear hybrid system under stochastic perturbations. By using the Lyapunov-type function, we proved that the almost surely exponential
stability remain be guaranteed as long as a bound on the maximum allowable transfer interval
(MATI) is satisfied.
Keywords:
Networked Control System, almost surely exponential stability, maximum allowable transfer interval, Lyapunov function.
References
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systems with communication delays, In Proceedings of the 48h IEEE Conference on Decision
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[7] X. Mao, Stochastic differential equations and applications, Elsevier, 2007.
[8] D. Nesic, D. Liberzon, A unified framework for design and analysis of networked and quantized
control systems, IEEE Trans. Automatic Control. 54 (2009) 732-747.
[9] P. Naghshtabrizi, J. P. Hespanha, A. R. Teel, Stability of delay impulsive systems with application to networked control systems, Transactions of the Institute of Measurement and Control.
32 (2010), 511-528.
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control systems, IEEE transactions on automatic control. 46 (2001) 1093-1097.
[11] G. C. Walsh, O. Beldiman, L. G. Bushnell, Error encoding algorithms for networked control
systems, Automatica. 38 (2002) 261-267.
[12] G. C. Walsh, H. Ye, L. G. Bushnell, Stability analysis of networked control systems, IEEE
transactions on control systems technology. 10 (2002) 438-446.
[13] L. Zhang, Y. Shi, T. Chen, B. Huang, A new method for stabilization of networked control
systems with random delays, IEEE Transactions on automatic control. 50 (2005) 1177-1181.
a lyapunov approach, In 2007 American Control Conference, IEEE. (2007) 1741-1746.
[2] D. Carnevale, A. R. Teel, D. Nesic, A Lyapunov proof of an improved maximum allowable transfer interval for networked control systems, IEEE Transactions on Automatic Control.
52 (2007) 892-897.
[3] D. Christmann, On the behavior of black bursts in tick-synchronized networks, Techn. Ber.
337 (2010).
[4] M. B. Cloosterman, N. Van de Wouw, W. P. M. H. Heemels, H. Nijmeijer, Stability of
networked control systems with uncertain time-varying delays, IEEE Transactions on Automatic
Controll. 54 (2009) 1575-1580.
[5] L. H. Duc, D. Christmann, R. Gotzhein, S. Siegmund, F. Wirth, The stability of try-oncediscard for stochastic communication channels: Theory and validation, In 2015 54th IEEE
Conference on Decision and Control (CDC). (2015) 4170-4175.
[6] W. P. M. H. Heemels, D. Nesic, A. R. Teel, N. Van de Wouw, Networked and quantized control
systems with communication delays, In Proceedings of the 48h IEEE Conference on Decision
and Control (CDC) held jointly with 2009 28th Chinese Control Conference. (2009) 7929-7935.
[7] X. Mao, Stochastic differential equations and applications, Elsevier, 2007.
[8] D. Nesic, D. Liberzon, A unified framework for design and analysis of networked and quantized
control systems, IEEE Trans. Automatic Control. 54 (2009) 732-747.
[9] P. Naghshtabrizi, J. P. Hespanha, A. R. Teel, Stability of delay impulsive systems with application to networked control systems, Transactions of the Institute of Measurement and Control.
32 (2010), 511-528.
[10] G. C. Walsh, O. Beldiman, L. G. Bushnell, Asymptotic behavior of nonlinear networked
control systems, IEEE transactions on automatic control. 46 (2001) 1093-1097.
[11] G. C. Walsh, O. Beldiman, L. G. Bushnell, Error encoding algorithms for networked control
systems, Automatica. 38 (2002) 261-267.
[12] G. C. Walsh, H. Ye, L. G. Bushnell, Stability analysis of networked control systems, IEEE
transactions on control systems technology. 10 (2002) 438-446.
[13] L. Zhang, Y. Shi, T. Chen, B. Huang, A new method for stabilization of networked control
systems with random delays, IEEE Transactions on automatic control. 50 (2005) 1177-1181.