access icon free pth moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay

The authors are concerned with the stability of hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Under some reasonable conditions, they establish an upper bound on the duration between two consecutive state observations. Moreover, we can design the discrete-time state feedback control to stabilise the given hybrid stochastic differential equations in the sense of pth moment exponential stability by developing a new theory. In comparison to the results given in the previous literature, this study has two new characteristics: (i) the stability criterion concerns pth moment exponential stability, which is different from the existing works; (ii) discrete-time state observations depend on time delays.

Inspec keywords: stochastic processes; differential equations; asymptotic stability; control system synthesis; stability criteria; delays; discrete time systems; state feedback

Other keywords: upper bound; stability criterion; discrete-time state feedback control design; discrete-time state observations; time delay; hybrid stochastic differential equation stability; pth moment exponential stabilisation

Subjects: Discrete control systems; Other topics in statistics; Differential equations (numerical analysis); Stability in control theory; Control system analysis and synthesis methods; Distributed parameter control systems

References

    1. 1)
      • 17. Qiu, Q., Liu, W., Hu, L.: ‘Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay’, Stat. Probab. Lett., 2016, 115, pp. 1626.
    2. 2)
      • 20. Mao, X.: ‘Stochastic differential equations and their applications’ (Horwood Publication, Chichester, 2007, 2nd edn.).
    3. 3)
      • 12. Mao, X., Lam, J., Huang, L.: ‘Stabilisation of hybrid stochastic differential equations by delay feedback control’, Syst. Control Lett., 2008, 57, pp. 927935.
    4. 4)
      • 9. Zhu, Q., Xi, F., Li, X.: ‘Robust exponential stability of stochastically nonlinear jump systems with mixed time delays’, J. Optim. Theory Appl., 2012, 154, pp. 154174.
    5. 5)
      • 14. Mao, X., George Yin, G., Yuan, C.: ‘Stabilization and destabilization of hybrid systems of stochastic differential equations’, Automatica, 2007, 43, pp. 264273.
    6. 6)
      • 18. Chen, W., Xu, S., Zou, Y.: ‘Stabilization of hybrid neutral stochastic differential delay equations by delay feedback control’, Syst. Control Lett., 2016, 88, pp. 113.
    7. 7)
      • 7. Zhu, Q.: ‘pth moment exponential stability of impulsive stochastic functional differential equations with Markovian switching’, J. Franklin Inst., 2014, 351, pp. 39653986.
    8. 8)
      • 10. Zhu, Q., Cao, J.: ‘Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays’, IEEE Trans. Neural Netw. Learn. Syst., 2012, 23, pp. 467479.
    9. 9)
      • 4. Shaikhet, L.: ‘Stability of stochastic hereditary systems with Markov switching’, Theory Stoch. Process., 1996, 2, (18), pp. 180184.
    10. 10)
      • 11. Mao, X., Yuan, C.: ‘Stochastic differential equations with Markovian switching’ (Imperial College Press, 2006).
    11. 11)
      • 3. Mao, X., Yin, G., Yuan, C.: ‘Stabilization and destabilization of hybrid systems of stochastic differential equations’, Automatica, 2007, 43, pp. 264273.
    12. 12)
      • 1. Ji, Y., Chizeck, H.J.: ‘Controllability, stabilizability and continuous-time Markovian jump linear quadratic control’, IEEE Trans. Autom. Control, 1990, 35, pp. 777788.
    13. 13)
      • 15. Mao, X.: ‘Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control’, Automatica, 2013, 49, (12), pp. 36773681.
    14. 14)
      • 19. Song, G., Zeng, B., Luo, Q., et al: ‘Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode’, IET Control Theory Appl., 2017, 11, pp. 301307.
    15. 15)
      • 2. Mariton, M.: ‘Jump linear systems in automatic control’ (Marcel Dekker, 1990).
    16. 16)
      • 13. Deng, F., Luo, Q., Mao, X.: ‘Stochastic stabilization of hybrid differential equations’, Automatica, 2012, 48, pp. 23212328.
    17. 17)
      • 8. Zhu, Q.: ‘Razumikhin-type theorem for stochastic functional differential equations with Le´vy noise and Markov switching’, Int. J. Control, 2017, 90, (8) pp. 17031712.
    18. 18)
      • 6. Kao, Y., Zhu, Q., Qi, W.: ‘Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching’, Appl. Math. Comput., 2015, 271, pp. 795804.
    19. 19)
      • 5. Mao, X.: ‘Stability of stochastic differential equations with Markovian switching’, Stoch. Process. Appl., 1999, 79, pp. 4567.
    20. 20)
      • 16. Mao, X., Liu, W., Hu, L., et al: ‘Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations’, Syst. Control Lett., 2014, 73, pp. 8895.
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