Stability Analysis of Homogeneous Uncertain Bilinear Systems with Non-Commensurate Time Delays

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 293)

Abstract

The problem of stability analysis for homogeneous uncertain bilinear systems subjected to non-commensurate time delays is considered in this paper. Several delay-dependent and delay-independent criteria are presented to guarantee the asymptotic stability of the overall systems. Furthermore, the decay rate is also estimated.

Keywords

Homogeneous bilinear system Non-commensurate time delays Uncertainty Decay rate 

References

  1. 1.
    Bacic, M., Cannon, M., & Kouvaritakis, B. (2003). Constrained control of SISO bilinear system. IEEE Transactions on Automatic Control, 48, 1443–1447.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Chabour, O., & Vivalda, J. C. (2000). Remark on local and global stabilization of homogeneous bilinear systems. Systems and Control Letters, 41, 141–143.CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Chen, M. S., & Tsao, S. T. (2000). Exponential stabilization of a class of unstable bilinear systems. IEEE Transactions on Automatic Control, 45, 989–992.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Chen, Y. P., Chang, J. L., & Lai, K. M. (2000). Stability analysis and bang-bang sliding control of a class of single-input bilinear systems. IEEE Transactions on Automatic Control, 45, 2150–2154.CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Chiou, J. S., Kung, F. C., & Li, T. H. S. (2000). Robust stabilization of a class of singular perturbed discrete bilinear systems. IEEE Transactions on Automatic Control, 45, 1187–1191.CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Coppel, W. A. (1965). Stability and asymptotic behavior of differential equations. Boston: D. C. Heath.MATHGoogle Scholar
  7. 7.
    Guojun, J. (2001). Stability of bilinear time-delay systems. IMA Journal of Mathematical Control and Information, 18, 53–60.CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Ho, D. W. C., Lu, G., & Zheng, Y. (2002). Global stabilization for bilinear systems with time delay. IEEE Proceedings of Control Theory and Application, 149, 89–94.CrossRefGoogle Scholar
  9. 9.
    Jerbi, H. (2001). Global feedback stabilization of new class of bilinear systems. Systems and Control Letters, 42, 313–320.CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Tao, C. W., Wang, W. Y., & Chan, M. L. (2004). Design of sliding mode controllers for bilinear systems with time varying uncertainties. IEEE Transactions on Systems, Man, and Cybernetics: Part B, 34, 639–645.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.General Educational CenterChung Hwa University of Medical TechnologyTainan CountyTaiwan, Republic of China

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