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\(H_{\infty }\) Static Output Control of Discrete-Time Networked Control Systems with an Event-Triggered Scheme

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Abstract

This paper is devoted to the event-triggered \(H_{\infty }\) static output feedback control of linear discrete-time networked control systems. With the help of zero-holder, a time-delay formulation is adopted to describe the even-triggered output. Resorting to Finsler lemma and time-delay techniques, a co-design framework of event-triggering communication and static output controller is established in terms of linear matrix inequalities. Meanwhile, the required \(H_\infty \) performance could be ensured by the proposed framework. Two examples are supplied to verify the validity of the proposed method.

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References

  1. S.P. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishan, Linear Matrix Inequalities in Systems and Control Theory (SIAM, Philadelphia, PA, 1994)

    Book  Google Scholar 

  2. D.U. Campos-Delgado, A.J. Rojas, J.M. Luna-Rivera, C.A. Gutierrez, Event-triggered feedback for power allocation in wireless networks. IET Control Theory Appl. 9, 2066–2074 (2015)

    Article  MathSciNet  Google Scholar 

  3. X. Chang, G. Yang, New results on output feedback control for linear discrete-time systems. IEEE Trans. Autom. Control 59, 1355–1359 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Cheng, F. Hao, Event-triggered control for linear descriptor systems. Circuits Syst. Signal Process. 32, 1065–1079 (2013)

    Article  MathSciNet  Google Scholar 

  5. J. Dong, G. Yang, Robust static output feedback control for linear discrete-time systems with time-varying uncertainties. Syst. Control Lett. 57, 123–131 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. S. Dong, H. Su, P. Shi, R. Lu, Z. Wu, Filtering for discrete-time switched fuzzy systems with quantization. IEEE Trans. Fuzzy Syst. doi:10.1109/TFUZZ.2016.2612699 (2016)

  7. S. Dong, Z. Wu, P. Shi, H. Su, R. Lu, Reliable control of fuzzy systems with quantization and switched actuator failures. IEEE Trans. Syst. Man Cybern. Syst. doi:10.1109/TSMC.2016.2636222 (2016)

  8. M.C.F. Donkers, W.M.H. Heemels, Output-based event-triggered control with guaranteed-gain and improved and decentralized event-triggering. IEEE Trans. Autom. Control 57, 1362–1376 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. M.C.F. Donkers, W.M.H. Heemels, N. Van de Wouw, L. Hetel, Stability analysis of networked control systems using a switched linear systems approach. IEEE Trans. Autom. Control 56, 2101–2115 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Eqtami, D.V. Dimarogonas, K.J. Kyriakopoulos, Event-triggered control for discrete-time systems. In Proceedings of the 2010 American Control Conference (2010), pp. 4719–4724

  11. Z. Feng, W. Zheng, On extended dissipativity of discrete-time neural networks with time delay. IEEE Trans. Neural Netw. Learn. Syst. 26, 3293–3300 (2015)

    Article  MathSciNet  Google Scholar 

  12. Z. Feng, W. Zheng, L. Wu, Reachable set estimation of T–S fuzzy systems with time-varying delay. IEEE Trans. Fuzzy Syst. doi:10.1109/TFUZZ.2016.2586945 (2016)

  13. S. He, F. Liu, Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach. Nonlinear Dyn. 80, 1159–1171 (2015)

    Article  MATH  Google Scholar 

  14. W.M.H. Heemels, A.R. Teel, N. van de Wouw, D. Nesic, Networked control systems with communication constraints: tradeoffs between transmission intervals, delays and performance. IEEE Trans. Autom. Control 55, 1781–1796 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Hu, X. Yin, Y. Zhang, E.G. Tian, Event-triggered guaranteed cost control for uncertain discrete-time networked control systems with time-varying transmission delays. IET Control Theory Appl. 6, 2793–2804 (2015)

    Article  MathSciNet  Google Scholar 

  16. B. Jiang, P. Shi, Z. Mao, Sliding mode observer-based fault estimation for nonlinear networked control systems. Circuits Syst. Signal Process. 30, 1–16 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. C. Liu, F. Hao, Dynamic output-feedback control for linear systems by using event-triggered quantisation. IET Control Theory Appl. 9, 1254–1263 (2015)

    Article  MathSciNet  Google Scholar 

  18. L. Lu, Y. Zou, Y. Niu, Event-driven robust output feedback control for constrained linear systems via model predictive control method. Circuits Syst. Signal Process. doi:10.1007/s00034-016-0316-51-16 (2016)

  19. J. Lunze, D. Lehmann, A state-feedback approach to event-based control. Automatica 46, 211–215 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. M.S. Mahmoud, M. Sabih, M. Elshafei, Event-triggered output feedback control for distributed networked systems. ISA Trans. 60, 294–302 (2016)

    Article  Google Scholar 

  21. P. Ogren, E. Fiorelli, N.E. Leonard, Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed environment. IEEE Trans. Autom. Control 49, 1292–1302 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  22. C. Peng, T. Yang, Event-triggered communication and \(H_{\infty }\) control co-design for networked control systems. Automatica 49, 1326–1332 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. C. Peng, J. Zhang, Event-triggered output-feedback \(H_{\infty }\) control for networked control systems with time-varying sampling. IET Control Theory Appl. 9, 1384–1391 (2015)

    Article  MathSciNet  Google Scholar 

  24. R. Postoyan, P. Tabuada, D. Nesic, A. Anta, A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans. Autom. Control 60, 982–996 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  25. M. Sato, Gain-scheduled output-feedback controllers depending solely on scheduling parameters via parameter-dependent Lyapunov functions. Automatica 47, 2786–2790 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: application to time-delay systems. Automatica 49, 2860–2866 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. M. Shen, S. Yan, G. Zhang, A new approach to event-triggered static output feedback control of networked control systems. ISA Trans. 65, 468–474 (2016)

    Article  Google Scholar 

  28. M. Shen, D. Ye, A finite frequency approach to control of Markov jump linear systems with incomplete transition probabilities. Appl. Math. Comput. 295, 53–64 (2017)

    MathSciNet  Google Scholar 

  29. J. Song, S. He, F. Liu, Y. Niu, Z. Ding, Data-driven policy iteration algorithm for optimal control of continuous-time Itô stochastic systems with Markovian jumps. IET Control Theory Appl. 10, 1431–1439 (2016)

    Article  MathSciNet  Google Scholar 

  30. W. Sun, H. Gao, O. Kaynak, Finite frequency \(H_{\infty }\) control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 19, 416–422 (2011)

    Article  Google Scholar 

  31. W. Sun, J. Li, Y. Zhao, H. Gao, Vibration control for active seat suspension systems via dynamic output feedback with limited frequency characteristic. Mechatronics 21, 250–260 (2011)

    Article  Google Scholar 

  32. W. Sun, Y. Zhao, J. Li, L. Zhang, H. Gao, Active suspension control with frequency band constraints and actuator input delay. IEEE Trans. Ind. Electron. 59, 530–537 (2012)

    Article  Google Scholar 

  33. P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52, 1680–1685 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  34. P. Tallapragada, N. Chopra, Event-triggered dynamic output feedback control for LTI systems. in 51st IEEE Conference on Decision and Control, Maui, Hawaii, USA (2012). pp. 6597–6602

  35. S. Tarbouriech, A. Seuret, J.M.G. da Silva Jr., D. Sbarbaro, Observer-based event-triggered control co-design for linear systems. IET Control Theory Appl. 10, 2466–2473 (2016)

    Article  MathSciNet  Google Scholar 

  36. G. Yang, D. Ye, Reliable control of linear systems with adaptive mechanism. IEEE Trans. Autom. Control 55, 242–247 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  37. D. Yue, E. Tian, Q. Han, A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans. Autom. Control 58, 475–481 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the editor, the associate editor and the reviewers for their valuable comments and suggestions which help to significantly improve the quality and presentation of this paper. This work was supported in part by the National Natural Science Foundation of China under Grant 61403189, in part by the Natural Science Foundation of Jiangsu Province of China under Grant BK20130949, in part by the Outstanding Youth Science Fund Award of Jiangsu Province under Grant BK20140045, in part by the Doctoral Foundation of Ministry of Education of China under Grant 20133221120012, in part by the Jiangsu Postdoctoral Science Foundation under Grant1401015B, in part by the China Postdoctoral Science Foundation under Grant 2015M570397, in part by the peak of six talents in Jiangsu Province under Grant 2015XXRJ-011, in part by the Key Laboratory Open Foundation under Grant MCCSE2015A03, in part by the Jiangsu Government Scholarship for Overseas Studies JS-2014046.

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Authors and Affiliations

  1. College of Electrical Engineering and Control Science, Nanjing Technology University, Nanjing, 211816, People’s Republic of China

    Shen Yan, Guangming Zhang, Mouquan Shen & Lingchun Li

  2. School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, People’s Republic of China

    Tao Li

  3. Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing, 210096, People’s Republic of China

    Mouquan Shen

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  1. Shen Yan
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  2. Guangming Zhang
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  3. Tao Li
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  4. Mouquan Shen
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  5. Lingchun Li
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Corresponding authors

Correspondence to Guangming Zhang or Mouquan Shen.

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Yan, S., Zhang, G., Li, T. et al. \(H_{\infty }\) Static Output Control of Discrete-Time Networked Control Systems with an Event-Triggered Scheme. Circuits Syst Signal Process 37, 553–568 (2018). https://doi.org/10.1007/s00034-017-0563-0

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