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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.
References
-
-
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. 16–26.
-
2)
-
20. Mao, X.: ‘Stochastic differential equations and their applications’ (Horwood Publication, Chichester, 2007, 2nd edn.).
-
3)
-
12. Mao, X., Lam, J., Huang, L.: ‘Stabilisation of hybrid stochastic differential equations by delay feedback control’, Syst. Control Lett., 2008, 57, pp. 927–935.
-
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. 154–174.
-
5)
-
14. Mao, X., George Yin, G., Yuan, C.: ‘Stabilization and destabilization of hybrid systems of stochastic differential equations’, Automatica, 2007, 43, pp. 264–273.
-
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. 1–13.
-
7)
-
7. Zhu, Q.: ‘pth moment exponential stability of impulsive stochastic functional differential equations with Markovian switching’, J. Franklin Inst., 2014, 351, pp. 3965–3986.
-
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. 467–479.
-
9)
-
4. Shaikhet, L.: ‘Stability of stochastic hereditary systems with Markov switching’, Theory Stoch. Process., 1996, 2, (18), pp. 180–184.
-
10)
-
11. Mao, X., Yuan, C.: ‘Stochastic differential equations with Markovian switching’ (Imperial College Press, 2006).
-
11)
-
3. Mao, X., Yin, G., Yuan, C.: ‘Stabilization and destabilization of hybrid systems of stochastic differential equations’, Automatica, 2007, 43, pp. 264–273.
-
12)
-
1. Ji, Y., Chizeck, H.J.: ‘Controllability, stabilizability and continuous-time Markovian jump linear quadratic control’, IEEE Trans. Autom. Control, 1990, 35, pp. 777–788.
-
13)
-
15. Mao, X.: ‘Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control’, Automatica, 2013, 49, (12), pp. 3677–3681.
-
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. 301–307.
-
15)
-
2. Mariton, M.: ‘Jump linear systems in automatic control’ (Marcel Dekker, 1990).
-
16)
-
13. Deng, F., Luo, Q., Mao, X.: ‘Stochastic stabilization of hybrid differential equations’, Automatica, 2012, 48, pp. 2321–2328.
-
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. 1703–1712.
-
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. 795–804.
-
19)
-
5. Mao, X.: ‘Stability of stochastic differential equations with Markovian switching’, Stoch. Process. Appl., 1999, 79, pp. 45–67.
-
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. 88–95.
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