## Abstract and Applied Analysis

### Fault Detection for Wireless Networked Control Systems with Stochastic Switching Topology and Time Delay

#### Abstract

This paper deals with the fault detection problem for a class of discrete-time wireless networked control systems described by switching topology with uncertainties and disturbances. System states of each individual node are affected not only by its own measurements, but also by other nodes’ measurements according to a certain network topology. As the topology of system can be switched in a stochastic way, we aim to design ${H}_{\infty }$ fault detection observers for nodes in the dynamic time-delay systems. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are acquired to guarantee the existence of the filters satisfying the ${H}_{\infty }$ performance constraint, and observer gains are derived by solving linear matrix inequalities. Finally, an illustrated example is provided to verify the effectiveness of the theoretical results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 879085, 13 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412278508

Digital Object Identifier
doi:10.1155/2014/879085

Mathematical Reviews number (MathSciNet)
MR3240568

Zentralblatt MATH identifier
07023242

#### Citation

Guo, Pengfei; Zhang, Jie; Karimi, Hamid Reza; Liu, Yurong; Wang, Yunji; Bo, Yuming. Fault Detection for Wireless Networked Control Systems with Stochastic Switching Topology and Time Delay. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 879085, 13 pages. doi:10.1155/2014/879085. https://projecteuclid.org/euclid.aaa/1412278508

#### References

• H. R. Karimi and H. Gao, “New delay-dependent exponential ${H}_{\infty }$ synchronization for uncertain neural networks with mixed time delays,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 40, no. 1, pp. 173–185, 2010.
• A. Ulusoy, O. Gurbuz, and A. Onat, “Wireless model-based predictive networked control system over cooperative wireless network,” IEEE Transactions on Industrial Informatics, vol. 7, no. 1,pp. 41–51, 2011.
• H. R. Karimi and P. Maass, “Delay-range-dependent exponential ${H}_{\infty }$ synchronization of a class of delayed neural networks,” Chaos, Solitons and Fractals, vol. 41, no. 3, pp. 1125–1135, 2009.
• H. R. Karimi, “Robust ${H}_{\infty }$ filter design for uncertain linear systems over network with network-induced delays and output quantization,” Modeling, Identification and Control, vol. 30, no. 1,pp. 27–37, 2009.
• J. Yu, F. Liu, X. Yu, C. Wu, and L. Wu, “Fault detection of discrete-time switched systems with distributed delays: input-output approach,” International Journal of Systems Science, vol. 44, no. 12, pp. 2255–2272, 2013.
• L. Wu, X. Yao, and W. X. Zheng, “Generalized ${H}_{2}$ fault detection for two-dimensional Markovian jump systems,” Automatica, vol. 48, no. 8, pp. 1741–1750, 2012.
• J. Chen and H. Zou, “An interesting method for the exponentials for some special matrices,” Systems Science and Control Engineering, vol. 2, no. 1, pp. 2–6, 2014.
• B. Zhang, C. Sconyers, C. Byington, R. Patrick, M. E. Orchard, and G. Vachtsevanos, “A probabilistic fault detection approach: application to bearing fault detection,” IEEE Transactions on Industrial Electronics, vol. 58, no. 5, pp. 2011–2018, 2011.
• N. Shih and C. Wang, “An inspection model of products and their input materials,” Systems Science and Control Engineering, vol. 2, no. 1, pp. 297–307, 2014.
• A. Tzes, G. Nikolakopoulos, and I. Koutroulis, “Development and experimental verification of a mobile client-centric networked controlled system,” European Journal of Control, vol. 11, no. 3, pp. 229–241, 2005.
• W. Zhou, C. Ji, J. Mou, D. Tong, and Y. Gao, “Adaptive target synchronization for wireless sensor networks with Markov delays and noise perturbation,” International Journal of Control, Automation and Systems, vol. 11, no. 5, pp. 919–925, 2013.
• J. Mou, W. Zhou, T. Wang, C. Ji, and D. Tong, “Consensus of thedistributed varying scale wireless sensor networks,” Mathematical Problems in Engineering, vol. 2013, Article ID 862518, 9 pages, 2013.
• W. Zhou, D. Tong, Y. Gao, C. Ji, and H. Su, “Mode and delay-dependent adaptive exponential synchronization in pth moment for stochastic delayed neural networks with Markovian switching,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 4, pp. 662–668, 2012.
• L. Liu, F. Wu, and W. Zhang, “Estimating parameters of s-systems by an auxiliary function guided coordinate descent method,” Systems Science and Control Engineering, vol. 2, no. 1, pp. 125–134, 2014.
• A.-L. Barabási, “Scale-free networks: a decade and beyond,” Science, vol. 325, no. 5939, pp. 412–413, 2009.
• S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “Complex networks: structure and dynamics,” Physics Reports, vol. 424, no. 4-5, pp. 175–308, 2006.
• J. P. Thiery and J. P. Sleeman, “Complex networks orchestrate epithelial-mesenchymal transitions,” Nature Reviews Molecular Cell Biology, vol. 7, no. 2, pp. 131–142, 2006.
• P. Lin and Y. Jia, “Average consensus in networks of multi-agents with both switching topology and coupling time-delay,” Physica A: Statistical Mechanics and Its Applications, vol. 387, no. 1, pp. 303–313, 2008.
• Z. Wang, Y. Wang, and Y. Liu, “Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 11–25, 2010.
• H. R. Karimi, “A sliding mode approach to ${H}_{\infty }$ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties,” Journal of the Franklin Institute, vol. 349, no. 4, pp. 1480–1496, 2012.
• Z. Wang, Y. Liu, and X. Liu, “Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1656–1662, 2010.
• H. R. Karimi, “Robust delay-dependent ${H}_{\infty }$ control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and Markovian switching parameters,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 58, no. 8, pp. 1910–1923, 2011.
• Z. Wang, Y. Liu, M. Li, and X. Liu, “Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 17, no. 3, pp. 814–820, 2006.
• J. Zhao, D. J. Hill, and T. Liu, “Synchronization of complex dynamical networks with switching topology: a switched system point of view,” Automatica, vol. 45, no. 11, pp. 2502–2511, 2009.
• J. Liang, Z. Wang, and X. Liu, “Distributed state estimation for uncertain Markov-type sensor networks with mode-dependent distributed delays,” International Journal of Robust and Nonlinear Control, vol. 22, no. 3, pp. 331–346, 2012.
• Z. Ji, Z. Wang, H. Lin, and Z. Wang, “Controllability of multi-agent systems with time-delay in state and switching topology,” International Journal of Control, vol. 83, no. 2, pp. 371–386, 2010.
• Y. Liu, Z. Wang, and X. Liu, “On global stability of delayed bam stochastic neural networks with Markovian switching,” Neural Processing Letters, vol. 30, no. 1, pp. 19–35, 2009.
• T. H. Lee, D. H. Ji, J. H. Park, and H. Y. Jung, “Decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network with randomly switching topology,” Applied Mathematics and Computation, vol. 219, no. 3, pp. 996–1010, 2012.
• Y. Liu, Z. Wang, and X. Liu, “State estimation for discrete-time neural networks with markov-mode-dependent lower and upper bounds on the distributed delays,” Neural Processing Letters, vol. 36, no. 1, pp. 1–19, 2012.
• J. Hu, Z. Wang, H. Gao, and L. K. Stergioulas, “Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 3008–3015, 2012.
• M. Lefebvre and F. Zitouni, “Analytical solutions to lqg homing problems in one dimension,” Systems Science and Control Engineering, vol. 2, no. 1, pp. 41–47, 2014.
• G. P. Samanta, “Analysis of a delayed hand-foot-mouth disease epidemic model with pulse vaccination,” Systems Science and Control Engineering, vol. 2, no. 1, pp. 61–73, 2014.
• L. Wu, C. Wang, and Q. Zeng, “Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems,” Journal of the Franklin Institute, vol. 345, no. 3, pp. 233–253, 2008.
• X. Su, P. Shi, L. Wu, and Y. Song, “A novel control design on discrete-time takagi-sugeno fuzzy systems with time-varying delays,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 4, pp. 655–671, 2013.
• L. Wu and W. X. Zheng, “Passivity-based sliding mode control of uncertain singular time-delay systems,” Automatica, vol. 45, no. 9, pp. 2120–2127, 2009.
• B. Shen, Z. Wang, and X. Liu, “Bounded ${H}_{\infty }$ synchronizationand state estimation for discrete time-varying stochastic complex networks over a finite horizon,” IEEE Transactions on Neural Networks, vol. 22, no. 1, pp. 145–157, 2011.
• H. Dong, Z. Wang, and H. Gao, “Robust ${H}_{\infty }$ filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts,” IEEE Transactions onSignal Processing, vol. 58, no. 4, pp. 1957–1966, 2010.
• H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Robust ${H}_{\infty }$ filtering for Markovian jump systems with randomly occurring nonlinearities and sensor saturation: the finite-horizon case,” IEEE Transactions on Signal Processing, vol. 59, no. 7, pp. 3048–3057, 2011.
• Z. Wang, D. W. C. Ho, Y. Liu, and X. Liu, “Robust ${H}_{\infty }$ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements,” Automatica, vol. 45, no. 3, pp. 684–691, 2009.
• B. Shen, Z. Wang, Y. S. Hung, and G. Chesi, “Distributed ${H}_{\infty }$ filtering for polynomial nonlinear stochastic systems in sensor networks,” IEEE Transactions on Industrial Electronics, vol. 58, no. 5, pp. 1971–1979, 2011.
• Z. Wang, D. W. C. Ho, and X. Liu, “Variance-constrained filtering for uncertain stochastic systems with missing measurements,” IEEE Transactions on Automatic Control, vol. 48, no. 7, pp. 1254–1258, 2003. \endinput