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\(\mathcal {H}_{\infty }\) Control of Time-Delayed Markov Jump Systems Subject to Mismatched Modes and Interval Conditional Probabilities

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Abstract

The \(\mathcal {H}_{\infty }\) control problem is studied for discrete-time Markov jump systems with both discrete and distributed delays. The controller to be designed allows for mode mismatch with the plant, and the mode mismatch behavior is described by a hidden Markov model. The conditional probabilities are permitted to be uncertain, which belong to an interval with precise upper and lower bounds. A sufficient condition that ensures the stochastic stability and \(\mathcal {H}_{\infty }\) disturbance-attenuation performance of the system is derived by employing a Lyapunov functional involving multiple quadratic items associated with the system modes. Then, two design methods are proposed for the desired controller. The first method does not utilize the property that the row sum of the conditional probability matrix is one, while the second method incorporates this property into the design process. The scenario where all the conditional probabilities are known in advance is also investigated, and corresponding controller design methods are presented. Finally, two examples are applied to validate the effectiveness of the design methods.

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References

  1. Gray, W.S.; González, O.R.; Dogan, M.: Stability analysis of digital linear flight controllers subject to electromagnetic disturbances. IEEE. Trans. Aerosp. Electron. Syst. 36(4), 1204–1218 (2000)

    Article  Google Scholar 

  2. Zhang, L.; Litong, R.; Xie, S.; Zhang, Y.; Wang, L.; Zhang, X.: Bi-index constraints-based output feedback fault-tolerant control for aero-engine distributed control systems. Arab. J Sci. Eng. 42(7), 2937–2946 (2017)

    Article  MathSciNet  Google Scholar 

  3. Ugrinovskii, V.; Pota, H.R.: Decentralized control of power systems via robust control of uncertain Markov jump parameter systems. Int. J. Control. 78(9), 662–677 (2005)

    Article  MathSciNet  Google Scholar 

  4. Deriche, M.; Abo absa, A.H.: A two-stage hierarchical bilingual emotion recognition system using a hidden Markov model and neural networks. Arab. J. Sci. Eng. 42, 5231–5249 (2017)

  5. Wu, X.; Shi, P.; Tang, Y.; Mao, S.; Qian, F.: Stability analysis of semi-Markov jump stochastic nonlinear systems. IEEE Trans. Autom. Control. 67(4), 2084–2091 (2022)

    Article  MathSciNet  Google Scholar 

  6. Cong, S.: Mode-independent switching stabilizing control for continuous-time linear Markovian switching systems. IEEE Trans. Auto. Control. (2023). https://doi.org/10.1109/TAC.2023.3255139

  7. Sathishkumar, M.; Sakthivel, R.; Kwon, O.M.; Kaviarasan, B.: Finite-time mixed \(\cal{H} _{\infty }\) and passive filtering for Takagi-Sugeno fuzzy nonhomogeneous Markovian jump systems. Int J. Syst. Sci. 48(7), 1416–1427 (2017)

    Article  MathSciNet  Google Scholar 

  8. Wu, W.; He, L.; Yan, Z.; Zhou, J.: Event-triggered extended dissipativity stabilization of semi-Markov switching systems. Appl. Math. Model. 118, 618–640 (2023)

    Article  MathSciNet  Google Scholar 

  9. Xu, C.; Tong, D.; Chen, Q.; Zhou, W.; Shi, P.: Exponential stability of Markovian jumping systems via adaptive sliding mode control. IEEE Trans. Syst. Man. Cybern. Syst. 51(2), 954–964 (2021)

    Article  Google Scholar 

  10. Jiang, B.; Liu, D.; Karimi, H.R.; Li, B.: Observer-based event-triggered H-infinity sliding control of Markovian jump system suffer from actuator attacks. Asian J. Control 25(4), 2975–2987 (2023)

    Article  MathSciNet  Google Scholar 

  11. Dong, S.; Chen, G.; Liu, M.; Wu, Z.G.: Robust adaptive \(\cal{H} _{\infty }\) control for networked uncertain semi-Markov jump nonlinear systems with input quantization. Sci. China Inf. Sci. 65, 1–2 (2022)

    Article  MathSciNet  Google Scholar 

  12. Mallik, W.; Santra, S.: Mitigation of vortex-induced vibration lock-in using time-delay closed-loop control. Nonlinear Dyn. 100, 1441–1456 (2020)

    Article  Google Scholar 

  13. Wang, S.; Yin, X.; Zhang, Y.; Li, P.; Wen, H.: Event-triggered cognitive control for networked control systems subject to DoS attacks and time delay. Arab. J. Sci. Eng. 48(5), 6991–7004 (2023)

    Article  Google Scholar 

  14. Gunasekaran, N.; Thoiyab, N.M.; Zhu, Q.; Cao, J.; Muruganantham, P.: New global asymptotic robust stability of dynamical delayed neural networks via intervalized interconnection matrices. IEEE Trans. Cybern. 52(11), 11794–11804 (2022)

    Article  Google Scholar 

  15. Tai, W.; Li, X.; Zhou, J.; Arik, S.: Asynchronous dissipative stabilization for stochastic Markov-switching neural networks with completely-and incompletely-known transition rates. Neural. Netw. 161, 55–64 (2023)

    Article  Google Scholar 

  16. Chen, G.; Yang, J.; Zhou, X.: Finite-time dissipative control for discrete-time stochastic delayed systems with Markovian switching and interval parameters. Commun Nonlinear Sci. Num. Simul. 110, 106352 (2022)

    Article  MathSciNet  Google Scholar 

  17. Sakthivel, R.; Sathishkumar, M.; Mathiyalagan, K.; Anthoni, S.M.: Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties. Int J. Adapt. Control Signal Process 31(1), 39–53 (2017)

    Article  MathSciNet  Google Scholar 

  18. Kavikumar, R.; Sakthivel, R.; Kwon, O.M.; Kaviarasan, B.: Reliable non-fragile memory state feedback controller design for fuzzy Markov jump systems. Nonlinear Anal. Hybrid Syst. 35, 100828 (2020)

    Article  MathSciNet  Google Scholar 

  19. Zhang, H.; Chen, Z.; Zhao, N.; Xing, B.; Kalidass, M.: Adaptive neural dissipative control for Markovian jump cyber-physical systems against sensor and actuator attacks. J. Franklin Inst. 360(12), 7676–7698 (2023)

    Article  MathSciNet  Google Scholar 

  20. Yao, L.; Wang, Z.; Huang, X.; Li, Y.; Ma, Q.; Shen, H.: Stochastic sampled-data exponential synchronization of Markovian jump neural networks with time-varying delays. IEEE Trans. Neural. Netw. Learn. Syst. 34(2), 909–920 (2023)

    Article  MathSciNet  Google Scholar 

  21. Dong, S.; Liu, L.; Feng, G.; Liu, M.; Wu, Z.G.; Zheng, R.: Cooperative output regulation quadratic control for discrete-time heterogeneous multiagent Markov jump systems. IEEE Trans. Cybern. 52(9), 9882–9892 (2022)

    Article  Google Scholar 

  22. Zhou, J.; Dong, J.; Xu, S.: Asynchronous dissipative control of discrete-time fuzzy Markov jump systems with dynamic state and input quantization. IEEE Trans. Fuzzy. Syst. (2023). https://doi.org/10.1109/TFUZZ.2023.3271348

    Article  Google Scholar 

  23. Zhang, X.; Wang, H.; Stojanovic, V.; Cheng, P.; He, S.; Luan, X.; Liu, F.: Asynchronous fault detection for interval type-2 fuzzy nonhomogeneous higher level Markov jump systems with uncertain transition probabilities. IEEE Trans. Fuzzy. Syst. 30(7), 2487–2499 (2022)

    Article  Google Scholar 

  24. Tao, Y.Y.; Wu, Z.G.; Huang, T.; Chakrabarti, P.; Ahn, C.K.: Asynchronous event-triggered output-feedback control of singular Markov jump systems. IEEE Trans. Cybern. (2022). https://doi.org/10.1109/TCYB.2022.3217197

    Article  Google Scholar 

  25. Zeng, P.; Deng, F.; Wu, Z.H.; Zhang, T.; Gao, X.: Event-triggered multiasynchronous \(\cal{H} _{\infty }\) control for Markov jump systems with transmission delay. IEEE Trans. Cybern. (2023). https://doi.org/10.1109/TCYB.2023.3261937

    Article  Google Scholar 

  26. Lin, Y.; Zhuang, G.; Xia, J.; Sun, W.; Zhao, J.: Asynchronous \(\cal{H} _{\infty }\) dynamic output feedback control for Markovian jump neural networks with time-varying delays. Int. J. Control. Autom. Syst. 20(3), 909–923 (2022)

    Article  Google Scholar 

  27. Zhang, M.; Shi, P.; Liu, Z.; Cai, J.; Su, H.: Dissipativity-based asynchronous control of discrete-time Markov jump systems with mixed time delays. Int. J. Robust Nonlinear Control 28(6), 2161–2171 (2018)

    Article  MathSciNet  Google Scholar 

  28. Shan, Y.; She, K.; Zhong, S.; Cheng, J.; Yu, Y.; Deng, H.: Asynchronous \(\cal{H} _{\infty }\) control of Markov jump discrete-time systems with incomplete transition probability and unreliable links. ISA Trans. 122, 218–231 (2022)

    Article  Google Scholar 

  29. Xia, W.; Li, Y.; Li, Z.; Jia, X.; Chen, W.; Chen, H.: Event-triggered filtering for uncertain semi-Markov jump systems with time-varying delay by using quantized measurement. J. Franklin Inst. 359(13), 7091–7114 (2022)

    Article  MathSciNet  Google Scholar 

  30. Chang, X.H.; Xiong, J.; Li, Z.M.; Park, J.H.: Quantized static output feedback control for discrete-time systems. IEEE Trans. Ind. Inf. 14(8), 3426–3435 (2018)

    Article  Google Scholar 

  31. Sathishkumar, M.; Sakthivel, R.; Wang, C.; Kaviarasan, B.; Anthoni, S.M.: Non-fragile filtering for singular Markovian jump systems with missing measurements. Signal Process 142, 125–136 (2018)

    Article  Google Scholar 

  32. Qin, X.; Dong, J.; Zhou, J.; Jiang, T.: Designing asynchronous filter with uncertain conditional probabilities for periodic discrete-time Markov jump systems. Commun Nonlinear Sci. Num. Simul 121, 107242 (2023)

    Article  MathSciNet  Google Scholar 

  33. Zhou, J.; Liu, Y.; Xia, J.; Wang, Z.; Arik, S.: Resilient fault-tolerant anti-synchronization for stochastic delayed reaction-diffusion neural networks with semi-Markov jump parameters. Neural Netw 125, 194–204 (2020)

    Article  Google Scholar 

  34. Liu, Y.; Wang, Z.; Liang, J.; Liu, X.: Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(5), 1314–1325 (2008)

  35. Seuret, A.; Gouaisbaut, F.: Wirtinger-based integral inequality: Application to time-delay systems. Automatica. 49(9), 2860–2866 (2013)

  36. Park, P.; Ko, J.W.; Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica. 47(1), 235–238 (2011)

    Article  MathSciNet  Google Scholar 

  37. Zhou, K.; Khargonekar, P.P.: Robust stabilization of linear systems with norm-bounded time-varying uncertainty. Syst. Control Lett. 10(1), 17–20 (1988)

    Article  MathSciNet  Google Scholar 

  38. Zhou, J.; Park, J.H.; Shen, H.: Non-fragile reduced-order dynamic output feedback \(\cal{H} _{\infty }\) control for switched systems with average dwell-time switching. Int. J. Control. 89(2), 281–296 (2016)

    Article  MathSciNet  Google Scholar 

  39. Liu, Y.; Fang, Z.; Park, J.H.; Fang, F.: Quantized event-triggered synchronization of discrete-time chaotic neural networks with stochastic deception attack. IEEE Trans. Syst. Man Cybern. Syst. 53(7), 4511–4521 (2023)

    Article  Google Scholar 

  40. Zhou, J.;Xu, D.; Tai,W.; Ahn, C. K.: Switched event-triggered \(\cal{H}_{\infty }\) security control for networked systems vulnerable to aperiodic DoS attacks. IEEE Trans. Netw. Sci. Eng. 10(4), 2109–2123 (2023)

  41. Shen, Y.; Wu, Z.G.; Shi, P.; Shu, Z.; Karimi, H.R.: \(\cal{H} _{\infty }\) control of Markov jump time-delay systems under asynchronous controller and quantizer. Automatica. 99, 352–360 (2019)

    Article  MathSciNet  Google Scholar 

  42. Chen, H.; Liu, R.; He, P.; Li, Z.: Asynchronous dissipative control for networked time-delay Markov jump systems with event-triggered scheme and packet dropouts. EURASIP J. Wireless Commun. Netw. 2022(1), 82 (2022)

  43. Palm, R.; Driankov, D.: Fuzzy switched hybrid systems-modeling and identification. In Proceedings of the 1998 IEEE International Symposium on Intelligent Control (ISIC) held jointly with IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA) Intell, pages 130–135. IEEE, (1998)

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Acknowledgements

This work was supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Grant nos. 2022AH050310 and 2022AH050290).

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  1. School of Computer Science & Technology, Anhui University of Technology, Ma’anshan, 243032, China

    Xueli Qin, Jingjing Dong, Xiaoqing Zhang, Taiping Jiang & Jianping Zhou

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Qin, X., Dong, J., Zhang, X. et al. \(\mathcal {H}_{\infty }\) Control of Time-Delayed Markov Jump Systems Subject to Mismatched Modes and Interval Conditional Probabilities. Arab J Sci Eng 49, 7471–7486 (2024). https://doi.org/10.1007/s13369-023-08332-4

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