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Quantitative exponential stability and stabilisation of discrete-time Markov jump systems with multiplicative noises

Quantitative exponential stability and stabilisation of discrete-time Markov jump systems with multiplicative noises

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This study is concerned about the quantitative exponential stability (QES) and stabilisation of discrete-time Markov jump systems with multiplicative noises. First, the defects of exponential stability in practical applications are analysed. Based on this analysis, a concept of the QES is given, and two stability criteria are derived. By utilising an auxiliary definition of general finite-time stability (GFTS), the relations among QES, GFTS and finite-time stability are established. Moreover, the quantitative exponential stabilisation is studied, and state feedback controller and the observer-based controller are designed. Subsequently, the relation between the states' upper bound and states' decay rate of considered systems is quantitatively shown by a searching method. Finally, an example is used to illustrate the effectiveness of the authors' obtained results.

References

    1. 1)
      • 1. Trefethen, L.N., Trefethen, A.E., Reddy, S.C., et al.: ‘Hydrodynamic stability without eigenvalues’, Adv. Colloid Interface Sci., 1993, 261, pp. 578584.
    2. 2)
      • 2. Xu, S.Y., Chen, T., Lam, J.: ‘Robust H filtering for uncertain Markovian jump systems with mode-dependent time delays’, IEEE Trans. Autom. Control, 2003, 48, (5), pp. 900907.
    3. 3)
      • 3. Dong, J., Yang, G.: ‘Robust H2 control of continuous-time Markov jump linear systems’, Automatica, 2008, 44, (5), pp. 14311436.
    4. 4)
      • 4. Zhang, L.: ‘H estimation for discrete-time piecewise homogeneous Markov jump linear systems’, Automatica, 2009, 45, (11), pp. 25702576.
    5. 5)
      • 5. Ma, S., Boukas, E.: ‘A singular system approach to robust sliding mode control for uncertain Markov jump systems’, Automatica, 2009, 45, (11), pp. 27072713.
    6. 6)
      • 6. Shen, H., Park, J.H., Zhang, L., et al.: ‘Robust extended dissipative control for sampled-data Markov jump systems’, Inf. J. Control, 2014, 87, (8), pp. 15491564.
    7. 7)
      • 7. Zhu, S., Han, Q., Zhang, C.: ‘l1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: a linear programming approach’, Automatica, 2014, 50, (8), pp. 20982107.
    8. 8)
      • 8. Dragan, V., Morozan, T.: ‘Stability and robust stabilization to linear stochastic systems described by differential equations with Markovian jumping and multiplicative white noise’, Stochastic Anal. Appl., 2002, 20, pp. 3392.
    9. 9)
      • 9. Costa, O.L., Wanderlei, V.L.P.: ‘Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems’, Automatica, 2007, 43, (4), pp. 587597.
    10. 10)
      • 10. Wang, Z., Liu, Y., Liu, X.: ‘Exponential stabilisation of a class of stochastic systems with Markovian jump parameters and mode-dependent mixed time-delays’, IEEE Trans. Autom. Control, 2010, 55, pp. 16561662.
    11. 11)
      • 11. Deng, F., Luo, Q., Mao, X.: ‘Stochastic stabilization of hybrid differential equations’, Automatica, 2012, 48, (9), pp. 23212328.
    12. 12)
      • 12. Wu, Z.J., Yang, J., Shi, P.: ‘Adaptive tracking for stochastic nonlinear systems with Markovian switching’, IEEE Trans. Autom. Control, 2010, 55, (9), pp. 21352141.
    13. 13)
      • 13. Xu, S., Chen, T.: ‘Robust H control for uncertain discrete-time stochastic bilinear systems with Markovian switching’, Inf. J. Robust Nonlinear Control, 2005, 15, (5), pp. 201217.
    14. 14)
      • 14. Ma, H., Zhang, W., Hou, T.: ‘Infinite horizon H2/H control for discrete-time time-varying Markov jump systems with multiplicative noise’, Bul. Inst. Politeh. ‘Gheorghe Gheorghiu-Dej’ Bucur. Ser. Autom., 2012, 48, (7), pp. 14471454.
    15. 15)
      • 15. Yan, Z.G., Zhang, W., Zhang, G.: ‘Finite-time stability and stabilization of Itô stochastic systems with Markovian switching: mode-dependent parameters approach’, IEEE Trans. Autom. Control, 2015, 60, pp. 24282433.
    16. 16)
      • 16. Yan, Z.G., Park, J.H., Zhang, W.: ‘Finite-time guaranteed cost control for Itô stochastic Markovian jump systems with incomplete transition rates’, Int. J. Robust Nonlinear Control, 2017, 27, (1), pp. 6683.
    17. 17)
      • 17. Dragan, V., Morozan, T., Stocia, A.M.: ‘Mathematica methods in robust control of discrete-time linear stochastic systems’ (Springer, New York, 2010).
    18. 18)
      • 18. Shi, P., Li, F.: ‘A survey on Markovian jump systems: modelling and design’, Int. J. Control Autom. Syst., 2015, 13, (1), pp. 116.
    19. 19)
      • 19. Amato, F., Ariola, M.: ‘Finite-time control of discrete-time linear systems’, IEEE Trans. Autom. Control, 2005, 50, (5), pp. 724729.
    20. 20)
      • 20. Ghaoui, L.E., Oustry, F., Rami, M.A.: ‘A cone complementarity linearization algorithm for static output-feedback and related problems’, IEEE Trans. Autom. Control, 1997, 42, (8), pp. 11711176.
    21. 21)
      • 21. Wang, H., Liu, X., Liu, K.: ‘Robust adaptive neural tracking control for a class of stochastic nonlinear interconnected systems’, IEEE Trans. Neural Netw. Learn. Syst., 2016, 27, (3), pp. 510523.
    22. 22)
      • 22. Wang, H., Liu, P.X., Shi, P.: ‘Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems’, IEEE Trans. Cybern., 2017, DOI: 10.1109/TCYB. 2655501.
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