access icon free Finite horizon H 2/H control of time-varying stochastic systems with Markov jumps and (x, u, v)-dependent noise

This study investigates the finite horizon H 2/H control of time-varying stochastic Markov jump systems (SMJSs) with state, control and disturbance-dependent noise. Firstly, the stochastic bounded real lemma of SMJSs is established, which by itself has theoretical importance. Secondly, several necessary and sufficient conditions for H 2/H control of SMJSs are proposed by means of coupled generalised differential Riccati equations. Finally, two numerical examples are given to show the effectiveness of the obtained results.

Inspec keywords: Riccati equations; H∞ control; stochastic systems; Markov processes; differential equations

Other keywords: time-varying stochastic Markov jump systems; finite horizon H infinity control; disturbance-dependent noise; coupled generalised differential Riccati equations; stochastic bounded real lemma; SMJS

Subjects: Linear algebra (numerical analysis); Differential equations (numerical analysis); Optimal control; Time-varying control systems

References

    1. 1)
    2. 2)
    3. 3)
      • 20. Oksendal, B.: ‘Stochastic differential equations: an introduction with applications’ (Springer-Verlag, New York, 2003).
    4. 4)
    5. 5)
    6. 6)
    7. 7)
    8. 8)
      • 28. Li, X., Zhou, X.Y.: ‘Indefinite stochastic LQ controls with Markovian jumps in a finite horizon’, Commun. Inf. Syst., 2002, 2, (3), pp. 265282.
    9. 9)
    10. 10)
    11. 11)
    12. 12)
    13. 13)
      • 5. Mao, X., Yuan, C.: ‘Stochastic differential equations with Markovian switching’ (Imperial College Press, London, 2006).
    14. 14)
    15. 15)
      • 4. Mariton, M.: ‘Jump linear systems in automatic control’ (Marcel Dekker, New York, 1990).
    16. 16)
    17. 17)
    18. 18)
    19. 19)
      • 1. Mao, X.: ‘Stochastic differential equations and applications’ (Horwood, London, 1997).
    20. 20)
    21. 21)
    22. 22)
    23. 23)
    24. 24)
    25. 25)
    26. 26)
    27. 27)
    28. 28)
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.1070
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