Advertisement

Robust Stability Testing of Time-Delay Bilinear Systems with Nonlinear Norm-Bounded Uncertainties

  • Chien-Hua LeeEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 691)

Abstract

Here, the stability test criteria for bilinear systems subjected to nonlinear norm-bounded uncertainties and non-commensurate time delays is treated. By using differential inequality techniques, we develop two sufficient robust stability testing conditions for assuring the above systems are robustly stable. Moreover, the decay rate of the aforementioned systems is also measured.

Keywords

Robust stability Decay rate Homogeneous bilinear system Nonlinear norm-bounded uncertainty Non-commensurate time delays 

References

  1. 1.
    Bacic, M., Cannon, M., Kouvaritakis, B.: Constrained control of SISO bilinear system. IEEE Trans. Autom. Control 48, 1443–1447 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Berrahmoune, L.: Stabilization and decay estimate for distributed bilinear systems. Syst. Control Lett. 36, 167–171 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bruni, C., Pillo, G.D., Koch, G.: Bilinear system: an appealing class of nearly linear systems in theory and applications. IEEE Trans. Autom. Control 19, 334–348 (1974)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Chabour, O., Vivalda, J.C.: Remark on local and global stabilization of homogeneous bilinear systems. Syst. Control Lett. 41, 141–143 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Chen, Y.P., Chang, J.L., Lai, K.M.: Stability analysis and bang-bang sliding control of a class of single-input bilinear systems. IEEE Trans. Autom. Control 45, 2150–2154 (2002)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Chen, L.K., Mohler, R.R.: Stability analysis of bilinear systems. IEEE Trans. Autom. Control 36, 1310–1315 (1991)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Chen, M.S., Tsao, S.T.: Exponential stabilization of a class of unstable bilinear systems. IEEE Trans. Autom. Control 45, 989–992 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Chiou, J.S., Kung, F.C., Li, T.H.S.: Robust stabilization of a class of singular perturbed discrete bilinear systems. IEEE Trans. Autom. Control 45, 1187–1191 (2000)CrossRefzbMATHGoogle Scholar
  9. 9.
    Coppel, W.A.: Stability and asymptotic behavior of differential equations. D. C. Heath, Boston (1965)zbMATHGoogle Scholar
  10. 10.
    Goubet-Bartholomeus, A., Dambrine, M., Richard, J.P.: Stability of perturbed systems with time-varying delays. Syst. Control Lett. 31, 155–163 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Guojun, J.: Stability of bilinear time-delay systems. IMA J. Math. Control Inf. 18, 53–60 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Ho, D.W.C., Lu, G., Zheng, Y.: Global stabilization for bilinear systems with time delay. IEEE Proc. Control Theory Appl. 149, 89–94 (2002)CrossRefGoogle Scholar
  13. 13.
    Jamshidi, M.: A near-optimum controller for cold-rolling mills. Int. J. Control 16, 1137–1154 (1972)CrossRefGoogle Scholar
  14. 14.
    Jerbi, H.: Global feedback stabilization of new class of bilinear systems. Syst. Control Lett. 42, 313–320 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Kotsios, S.: A note on BIBO stability of bilinear systems. J. Franklin Inst. 332B, 755–760 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Lee, C.S., Leitmann, G.: Continuous feedback guaranteeing uniform ultimate boundness for uncertain linear delay systems: an application to river pollution control. Comput. Math. Appl. 16, 929–938 (1983)CrossRefzbMATHGoogle Scholar
  17. 17.
    Lee, C.H.: On the stability of uncertain homogeneous bilinear systems subjected to time-delay and constrained inputs. J. Chin. Inst. Eng. 31, 529–534 (2008)CrossRefGoogle Scholar
  18. 18.
    Lee, C.H.: New results for robust stability discrete bilinear uncertain time-delay systems. Circ. Syst. Sig. Process. 35, 79–100 (2016)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Lu, G., Ho, D.W.C.: Global stabilization controller design for discrete-time bilinear systems with time-delays. Proceedings of the 4th World Congress on Intelligent Control and Automation, pp. 10–14 (2002)Google Scholar
  20. 20.
    Mohler, R.R.: Bilinear control processes. Academic, New York (1973)zbMATHGoogle Scholar
  21. 21.
    Niculescu, S.I., Tarbouriceh, S., Dion, J.M., Dugard, L.: Stability criteria for bilinear systems with delayed state and saturating actuators. Proceedings of the 34th Conference on Decision & Control, pp. 2064–2069 (1995)Google Scholar
  22. 22.
    Tao, C.W., Wang, W.Y., Chan, M.L.: Design of sliding mode controllers for bilinear systems with time varying uncertainties. IEEE Trans. Syst. Man Cybern. Part B 34, 639–645 (2004)CrossRefGoogle Scholar
  23. 23.
    Smith, H.W.: Dynamic control of a two-stand cold mill. Automatica 5, 183–190 (1969)CrossRefGoogle Scholar
  24. 24.
    Wang, S.S., Chen, B.S., Lin, T.P.: Robust stability of uncertain time-delay systems. Int. J. Control 46, 963–976 (1987)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Cheng-Shiu UniversityKaohsiungTaiwan

Personalised recommendations