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access icon free Finite-time asynchronous control for positive discrete-time Markovian jump systems

Finite-time asynchronous control problem is discussed for positive Markovian jump systems in this study. The non-synchronous behaviours generated between the system modes and controller modes are fully considered. To ensure the closed-loop system positivity and finite-time boundedness with a guaranteed performance level, a sufficient condition on the existence of an asynchronous controller is first established by applying Lyapunov–Krasovskii functional approach and recursive matrix inequality methods. Then, with the aid of matrix conversions, the specific form of controller gain matrices can be constructed by solving linear matrix inequality (LMI) conditions. A numerical example is presented and application is illustrated to validate the proposed results by employing a pest's age-structured population dynamic model.


    1. 1)
      • 24. Xiang, M., Xiang, Z.R.: ‘Finite-time L1 control for positive switched linear systems with time-varying delay’, Commun. Nonlinear Sci. Numer. Simul., 2013, 18, pp. 31583166.
    2. 2)
      • 11. Shen, H., Li, F., Xu, S.Y., et al: ‘Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations’, IEEE Trans. Autom. Control, 2018, 63, pp. 27092714.
    3. 3)
      • 3. Hien, L.V.: ‘An LP approach to full-order and reduced-order state estimations of positive Markov jump systems with delay’, Int. J. Syst. Sci., 2017, 48, pp. 25342543.
    4. 4)
      • 22. Zhang, J.F., Han, Z.Z., Wu, H.: ‘Robust finite-time stability and stabilisation of switched positive systems’, IET Control Theory Appl., 2014, 8, pp. 6775.
    5. 5)
      • 26. Cao, X.Y., Liu, L.P., Fu, Z.M., et al: ‘Guaranteed cost finite-time control for positive switched linear systems with time-varying delays’, J. Control Sci. Eng., 2017, 2017, pp. 319328.
    6. 6)
      • 27. Wang, B., Zhu, S.Q., Xu, Y., et al: ‘Stochastic finite-time boundedness analysis and control for discrete-time positive Markov jump linear systems’. Proc. Chinese Control Decision Conf. (CCDC), Yinchuan, China, May 2016, pp. 18241829.
    7. 7)
      • 37. Zhang, J.F., Zhao, X.D., Fu, B., et al: ‘L1/l1-gain analysis and synthesis of Markovian jump positive systems with time delay’, ISA Trans., 2016, 63, pp. 93102.
    8. 8)
      • 29. Cheng, J., Chang, X.H., Park, J.H., et al: ‘Fuzzy-model-based H control for discrete-time switched systems with quantized feedback and unreliable links’, Inf. Sci., 2018, 436, pp. 181196.
    9. 9)
      • 10. Cheng, J., Park, J.H., Karimi, H.R., et al: ‘A flexible terminal approach to sampled-data exponentially synchronization of Markovian neural networks with time-varying delayed signals’, IEEE Trans. Cybern., 2018, 48, pp. 22322244.
    10. 10)
      • 7. Ren, H.L., Zong, G.D.: ‘Robust input-output finite-time filtering for uncertain Markovian jump nonlinear systems with partially known transition probabilities’, Int. J. Adapt Control Signal Process., 2017, 31, pp. 14371455.
    11. 11)
      • 1. Alicia, M.G., Antonio, M.S.R., Javier, G.G.: ‘Modeling and forecasting electricity prices with input/output hidden Markov models’, IEEE Trans. Power Syst., 2005, 20, pp. 1324.
    12. 12)
      • 6. Qi, W.H., Park, J.H., Cheng, J., et al: ‘Anti-windup design for stochastic Markovian switching systems with mode-dependent time-varying delays and saturation nonlinearity’, Nonlinear Anal. Hybrid Syst., 2017, 26, pp. 201211.
    13. 13)
      • 23. Chen, G.P., Yang, Y.: ‘Finite-time stability of switched positive linear systems’, Int. J. Robust Nonlinear Control, 2014, 24, pp. 179190.
    14. 14)
      • 19. Amato, F., Ariola, M., Dorato, P.: ‘Finite-time control of linear systems subject to parametric uncertainties and disturbances’, Automatica, 2001, 37, pp. 14591463.
    15. 15)
      • 35. Ren, H.L., Zong, G.D., Hamid Reza, K.: ‘Asynchronous finite-time filtering of networked switched systems and its application: an event-driven method’, IEEE Trans. Circuits Syst. Regul. Pap., 2018, 66, pp. 391402, DOI: 10.1109/TCSI.2018.2857771.
    16. 16)
      • 31. Wang, X.H., Zong, G.D., Sun, H.B.: ‘Asynchronous finite-time dynamic output feedback control for switched time-delay systems with nonlinear disturbance’, IET Control Theory Appl., 2016, 10, pp. 11421150.
    17. 17)
      • 4. Zong, G.D., Yang, D., Hou, L.L., et al: ‘Robust finite-time H control for Markovian jump systems with partially known transition probabilities’, J. Franklin Inst., 2013, 350, pp. 15621578.
    18. 18)
      • 2. Shen, H., Li, F., Wu, Z.G., et al: ‘Finite-time asynchronous H filtering for discrete-time Markov jump systems over a lossy network’, Int. J. Robust Nonlinear Control, 2016, 26, pp. 38313848.
    19. 19)
      • 15. Hien, L.V., Trinh, H.: ‘Delay-dependent stability and stabilisation of two-dimensional positive Markov jump systems with delays’, IET Control Theory Appl., 2017, 11, pp. 16031610.
    20. 20)
      • 28. Ding, S.H., Zheng, W.X., Sun, J.L., et al: ‘Second-order sliding mode controller design and its implementation for buck converters’, IEEE Trans. Ind. Electron., 2018, 14, pp. 19902000.
    21. 21)
      • 33. Wu, Z.G., Shi, P., Su, H.Y., et al: ‘Passivity-based asynchronous control for Markov jump systems’, IEEE Trans. Auto. Con., 2017, 62, pp. 20202025.
    22. 22)
      • 25. Duan, Z.X., Xiang, Z.R.: ‘Finite-time boundedness and l1-gain analysis for discrete positive switched systems with time-varying delay’. Proc. Chinese Control Conf. (CCC), Xi'an, China, July 2013, pp. 20902095.
    23. 23)
      • 32. Ren, Y., Er, M.J., Sun, G.H.: ‘Asynchronous l1 positive filter design for switched positive systems with overlapped detection delay’, IET Control Theory Appl., 2016, 11, pp. 319328.
    24. 24)
      • 8. Li, L.W., Yang, G.H.: ‘Stabilisation of Markov jump systems with input quantisation and general uncertain transition rates’, IET Control Theory Appl., 2017, 11, pp. 516523.
    25. 25)
      • 13. Farina, L., Rinaldi, S.: ‘Positive linear systems: theory and applications’ (John Wiley & Sons, New York, 2000).
    26. 26)
      • 5. Sun, H.B., Li, Y.K., Zong, G.D., et al: ‘Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities’, Automatica, 2018, 89, pp. 349357.
    27. 27)
      • 14. Zhang, D., Zhang, Q.L., Du, B.Z.: ‘Positivity and stability of positive singular Markovian jump time-delay system swith partially unknown transition rates’, J. Franklin Inst., 2016, 354, pp. 627649.
    28. 28)
      • 30. Ge, C., Wang, H., Liu, Y.J., et al: ‘Stabilization of chaotic systems under variable sampling and state quantized controller’, Fuzzy Sets Syst., 2018, 344, pp. 129144.
    29. 29)
      • 12. Wang, J., Liang, K., Huang, X., et al: ‘Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback’, Appl. Math. Comput., 2018, 328, pp. 247262.
    30. 30)
      • 18. Dorato, P.: ‘Short-time stability in linear time-varying systems’. Proc. of the IRE Int. Convention Record, Part 4, New York, NY, USA, 1961, pp. 8387.
    31. 31)
      • 20. Zhu, S.Q., Wang, B., Zhang, C.H.: ‘Delay-dependent stochastic finite-time l1-gain filtering for discrete-time positive Markov jump linear systems with time-delay’, Automatica, 2017, 354, pp. 68946913.
    32. 32)
      • 36. Zhu, S.Q., Han, Q.L., Zhang, C.H.: ‘Investigating the effects of time-delays on stochastic stability and designing l1-gain controllers for positive discrete-time Markov jump linear systems with time-delay’, Inf. Sci., 2016, 355, pp. 265281.
    33. 33)
      • 17. Qi, W.H., Zong, G.D., Karimi, H.R.: ‘L control for positive delay systems with semi-Markov process and application to a communication network model’, IEEE Trans. Ind. Electron., 2018, 66, pp. 20812091, DOI: 10.1109/TIE.2018.2838113.
    34. 34)
      • 9. Qi, W.H., Zong, G.D., Karimi, H.R.: ‘Observer-based adaptive SMC for nonlinear uncertain singular semi-Markov jump systems with applications to DC motor’, IEEE Trans. Circuits Syst. Regul. Pap., 2018, 65, pp. 29512960.
    35. 35)
      • 21. Liu, Y., Tao, W., Li, L.M., et al: ‘Finite-time boundedness and L2-gain analysis for switched positive linear systems with multiple time delays’, Int. J. Robust Nonlinear Control, 2017, 27, pp. 35083523.
    36. 36)
      • 16. Wang, J.Y., Qi, W.H., Gao, X.W.: ‘Positive observer design for positive Markovian jump systems with partly known transition rates’, J. Syst. Sci. Complex, 2017, 30, pp. 307315.
    37. 37)
      • 34. Wu, Z.G., Dong, S.L., Su, H.Y., et al: ‘Asynchronous dissipative control for fuzzy Markov jump systems’, IEEE Trans. Cybern., 2017, 48, pp. 24262436, DOI: 10.1109/TCYB.2017.2739754.

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