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Controllability and Observability of Stochastic Singular Systems in Banach Spaces

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Abstract

Exact (approximate) controllability and exact (approximate) observability of stochastic singular systems in Banach spaces are discussed. Firstly, the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces. Secondly, the necessary and sufficient conditions for the exact (approximate) controllability and exact (approximate) observability of the systems considered are derived in terms of GE-semigroup, and the dual principle is given. Thirdly, an illustrative example is given.

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References

  1. Melnikova I V, Filikov A I, and Anufrieva U A, Abstract stochastic equations. I. classical and distributional solutions, J. Math. Sciences, Functional Analysis, 2002, 111: 3430–3475.

    MathSciNet  MATH  Google Scholar 

  2. Vlasenko L A and Rutkas A G, Stochastic impulse control of parabolic systems of sobolev type, Differential Equations, 2011, 47: 1498–1507.

    Article  MathSciNet  Google Scholar 

  3. Kuttler K L and Li J, Generalized stochastic evolution equations, J. Differential Equations, 2014, 257: 816–842.

    Article  MathSciNet  Google Scholar 

  4. Liaskos K B, Pantelous A A, and Stratis I G, Linear stochastic degenerate Sobolev equations and applications, International Journal of Control, 2015, 88: 2538–2553.

    Article  MathSciNet  Google Scholar 

  5. Liaskos K B, Stratis I G, and Pantelous A A, Stochastic degenerate Sobolev equations: Well posedness and exact controllability, Math. Meth. App. Sci., 2018, 41: 1025–1032.

    Article  MathSciNet  Google Scholar 

  6. Dai L, Filting and LQG problems for discrete-time stochastic singular systems, IEEE Transactions on Automatic Control, 1989, 34: 1105–1108.

    Article  MathSciNet  Google Scholar 

  7. Gashi B and Pantelous A A, Linear backward stochastic differential equations of descriptor type: Regular systems, Stochastic Analysis and Applications, 2013, 31: 142–166.

    Article  MathSciNet  Google Scholar 

  8. Gao Z W and Shi X Y, Observer-based controller design for stochastic descriptor systems with Brownian motions, Automatica, 2013, 49: 2229–2235.

    Article  MathSciNet  Google Scholar 

  9. Gashi B and Pantelous A A, Linear stochastic systems of descriptor type: Theory and applications, safety, reliability, risk and life-cycle performance of structure and infrastructures, Proceedings of the 11th International Conference on Structure Safety and Reliability, ICOSSAR 2013, 2013, 1047–1054.

    Google Scholar 

  10. Gashi B and Pantelous A A, Linear backward stochastic differential systems of descriptor type with structure and applications to engineering, Probabilitic Engineering Mechanics, 2015, 40: 1–11.

    Article  Google Scholar 

  11. Zhang W H, Zhao Y, and Sheng L, Some remarks on stability of stochastic singular systems with state-dependent noise, Automatica, 2015, 51: 273–277.

    Article  MathSciNet  Google Scholar 

  12. Zhao Y and Zhang W H, New results on stability of singular stochastic Markov jump systems with state-dependent noise, International Journal of Robust and Nonlinear Control, 2016, 26: 2169–2186.

    Article  MathSciNet  Google Scholar 

  13. Xing S Y and Zhang Q L, Stability and exact observability of discrete stochastic singular systems based on generalized Lyapunov equations, IET Control Theory and Applications, 2016, 10: 971–980.

    Article  MathSciNet  Google Scholar 

  14. Zhang Q L, Li L, Yan X G, et al., Sliding mode control for singular stochastic Markovian jump systems with uncertainties, Automatica, 2017, 79: 27–34.

    Article  MathSciNet  Google Scholar 

  15. Zhuang G M, Ma Q, Zhang B Y, et al, Admissibility and stabilization of stochastic singular Markovian jump systems with time delays, Systems and Control Letters, 2018, 114: 1–10.

    Article  MathSciNet  Google Scholar 

  16. Zhao W Y, Ma Y C, Chen A H, et al., Robust sliding mode control for Markovian jump singular systems with randomly changing structure, Applied Mathematics and Computation, 2019, 349: 81–96.

    Article  MathSciNet  Google Scholar 

  17. Ge Z Q and Ge X C, An exact null controllability of stochastic singular systems, SCI CHINA Inf. Sci., 2021, 64: 179202:1–179202:3.

    MathSciNet  Google Scholar 

  18. Ge Z Q, Zhu G T, and Feng D X, Exact controllability for singular distributed parameter systems in Hilbert spaces, Sci. China Ser. F-Inf. Sci., 2009, 52: 2045–2052.

    Article  MathSciNet  Google Scholar 

  19. Ge Z Q and Feng D X, Well-posed problem of nonlinear singular distributed parameter systems and nonlinear GE-semigroups, Sci. China Inf. Sci., 2013, 56: 128201:1–128201:14.

    Article  MathSciNet  Google Scholar 

  20. Curtain R and Zwart H J, An Introduction to Infinite Dimensional Linear Systems Theory, Springer-Verlag, New York, 1995.

    Book  Google Scholar 

  21. Melnikova I V and Filinkov A I, Abstract Cauchy Problem, Chapnan and Hall/CRC, London, 2001, 86–91.

    Book  Google Scholar 

Download references

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Correspondence to Zhaoqiang Ge.

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This research was supported by the National Natural Science Foundation of China under Grant Nos. 11926402 and 61973338.

This paper was recommended for publication by Editor LI Xun.

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Ge, Z. Controllability and Observability of Stochastic Singular Systems in Banach Spaces. J Syst Sci Complex 35, 194–204 (2022). https://doi.org/10.1007/s11424-021-0164-7

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  • DOI: https://doi.org/10.1007/s11424-021-0164-7

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