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New Results for Robust Stability of Discrete Bilinear Uncertain Time-Delay Systems

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Abstract

In this paper, new results for the problem of the robust stability of discrete homogeneous bilinear time-delay systems subjected to nonlinear or parametric uncertainties are addressed. Applying a concise upper bound to the Lyapunov equation approach and then associating some linear algebraic techniques, several delay-independent conditions are presented to assure the robust stability of the aforementioned systems. One of the features of the present criteria is that they are independent of any Lyapunov equation, although the Lyapunov equation approach is adopted. Comparing to an existing work, it is shown that the obtained results are sharper. Finally, all obtained results are applied to solve the same problem of discrete bilinear uncertain systems and discrete time-delay systems with/without uncertainties. Concise criteria for the robust stability of the mentioned systems are developed, and comparisons between the obtained results and those appeared in the literature are also made. It is shown that all obtained results in this work are either tighter or more concise.

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References

  1. M. Bacic, M. Cannon, B. Kouvaritakis, Constrained control of SISO bilinear system. IEEE Trans. Autom. Control 48, 1443–1447 (2003)

    Article  MathSciNet  Google Scholar 

  2. O. Chabour, J.C. Vivalda, Remark on local and global stabilization of homogeneous bilinear systems. Syst. Control Lett. 41, 141–143 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. C.Y. Chen, C.H. Lee, Robust stability of homogeneous large-scale bilinear systems with time delays and uncertainties. J. Process Control 19, 1082–1090 (2009)

    Article  Google Scholar 

  4. Y.P. Chen, J.L. Chang, K.M. Lai, Stability analysis and bang-bang sliding control of a class of single-input bilinear systems. IEEE Trans. Autom. Control 45, 2150–2154 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. J.S. Chiou, F.C. Kung, T.H.S. Li, Robust stabilization of a class of singular perturbed discrete bilinear systems. IEEE Trans. Autom. Control 45, 1187–1191 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Guojun, Stability of bilinear time-delay systems. IMA J. Math. Control Inf. 18, 53–60 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. D.W.C. Ho, G. Lu, Y. Zheng, Global stabilization for bilinear systems with time delay. IEE Proc. Control Theory Appl. 149, 89–94 (2002)

    Article  Google Scholar 

  8. T.L. Hsien, C.H. Lee, Robust stability of discrete bilinear uncertain time-delay systems. Circuits Syst. Signal Proc. 30, 1417–1443 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. H. Jerbi, Global feedback stabilization of new class of bilinear systems. Syst. Control Lett. 42, 313–320 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. B.S. Kim, Y.J. Kim, M.T. Lim, Robust \(H_\infty \) state feedback control methods for bilinear systems. IEE Proc. Control Theory Appl. 152, 553–559 (2005)

    Article  Google Scholar 

  11. S. Lakshmanan, J.H. Park, H.Y. Jung, Robust delay-dependent stability criteria for dynamic systems with nonlinear perturbations and leakage delay. Circuits Syst. Signal Proc. 32, 1637–1657 (2013)

    Article  MathSciNet  Google Scholar 

  12. C.H. Lee, On the stability of uncertain homogeneous bilinear systems subjected to time-delay and constrained inputs. J. Chin. Inst. Eng. 31, 529–534 (2008)

    Article  Google Scholar 

  13. C.H. Lee, C.Y. Chen, Further results for robust stability of homogeneous large-scale bilinear systems with time delays and uncertainties. Comput. Math. Appl. 64, 1532–1544 (2012)

    Article  Google Scholar 

  14. C.H. Lee, C.Y. Chen, On the robust stability of discrete systems subjected to a time delay and uncertainties. ICIC Express Lett. 7, 1365–1370 (2013)

    MathSciNet  Google Scholar 

  15. J. Lian, F. Zhang, P. Shi, Sliding mode control of uncertain stochastic hybrid delay systems with average dwell time. Circuits Syst. Signal Proc. 33, 2719–2740 (2014)

    Article  Google Scholar 

  16. G. Lu, D. W. C. Ho, in Proceedings of the \(4{\rm th}\) World Congress on Intelligent Control and Automation. Global stabilization controller design for discrete-time bilinear systems with time-delays. (Shanghai, China, 2002), pp. 10–14

  17. G. Lu, D.W.C. Ho, Continuous stabilization controllers for singular bilinear systems: the state feedback case. Automatica 42, 309–314 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. T. Mori, N. Fukuma, M. Kuwahara, Delay-independent stability criteria for discrete-delay systems. IEEE Trans. Autom. Control 27, 964–966 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  19. S. B. Stojanovic, D. Lj. Debeljkovic, Stability of linear discrete time delay systems: Lyapunov-Krasovskii approach, in the \(4{\rm th}\) IEEE Conference on Industrial Electronics and Applications (ICIEA), (Xi’an, China 2009), pp. 2497–2501

  20. C.W. Tao, W.Y. Wang, M.L. Chan, Design of sliding mode controllers for bilinear systems with time varying uncertainties. IEEE Trans. Syst. Man Cybern. B 34, 639–645 (2004)

    Article  Google Scholar 

  21. M. Vidyasagar, Nonlinear system analysis, 2nd edn. (Printice-Hall, New Jersey, 1993)

    Google Scholar 

  22. W. Wang, S.K. Nguang, S. Zhong, New delay-dependent stability criteria for uncertain neutral system with time-varying delays and nonlinear perturbations. Circuits Syst. Signal Proc. 30, 941–961 (2011)

    Article  Google Scholar 

  23. X. Yang, L.K. Chen, Stability of discrete bilinear systems with time-delayed feedback functions. IEEE Trans. Autom. Contol 38, 158–163 (1993)

    Article  MATH  Google Scholar 

  24. W. Zhou, D. Tong, H. Lu, Time-delay dependent \(H_\infty \) model reduction for uncertain stochastic systems: continuous-time case. Circuits Syst. Signal Proc. 30, 941–961 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The author would like to thank the National Science Council, the Republic of China, for financial support of this research under the Grant NSC 101-2221-E-230-010.

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Authors and Affiliations

  1. Department of Electrical Engineering, Cheng-Shiu University, Kaohsiung, 833, Taiwan, Republic of China

    Chien-Hua Lee

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  1. Chien-Hua Lee
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Correspondence to Chien-Hua Lee.

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Lee, CH. New Results for Robust Stability of Discrete Bilinear Uncertain Time-Delay Systems. Circuits Syst Signal Process 35, 79–100 (2016). https://doi.org/10.1007/s00034-015-0055-z

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