Advertisement

Model and stability of hybrid linear system

  • Hong Seong Park
  • Young Sin Kim
  • Wook Hyun Kwon
  • Sang Jeong Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1066)

Abstract

This paper presents a hybrid model suitable for analysis of hybrid systems and for synthesis of hybrid controllers, and the linear hybrid system which combines continuous linear dynamics in each discrete state with discrete dynamics having the Markov property. The stochastic stability of the linear hybrid system is defined and the stability condition and the stabilizability condition is proposed. A simple example is given to illustrate the proposed framework.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K.J. Astrom and B. Wittenmark(1989), Adaptive Control, USA: Addison-Wesley Pub. Co.Google Scholar
  2. 2.
    A.Benveniste and P. Le Guernic(1990), Hybrid Dynamical Systems Theory and the SIGNAL Language, IEEE Trans. Automat. Contr., Vol. 35, No. 5, pp.535–546.CrossRefGoogle Scholar
  3. 3.
    M.S. Branicky(1993), Topology of Hybrid Systems, Proc. of the 32th Conf. Decision and Control, pp.2309–2314.Google Scholar
  4. 4.
    C.M. Özveren and A.S. Willsky(1991), Stability and Stabilizability of Discrete Event Dynamic, J. of ACM, vol. 38, No. 3, pp. 730–752.Google Scholar
  5. 5.
    L.Holloway and B.Krogh(1992), Properties of Behavioral Models for a Class of Hybrid Dynamical Systems, Proc. of the 31th Conf. Decision and Control, pp.3752–3757.Google Scholar
  6. 6.
    J.Y. Hung, W. Gao, and J.C. Hung(1993), Variable Structure Control: A Survey, IEEE Trans. on Industrial Electronics, Vol. 40, No. 1, pp.2–22.CrossRefGoogle Scholar
  7. 7.
    W.Kohn and A.Nerode(1992), Multiple Agent Autonomous Hybrid Control Systems, Proc. of the 31th Conf. Decision and Control, pp.2956–2966.Google Scholar
  8. 8.
    M.D. Lemmon, J.A. Stiver, and P.J. Antsaklis(1993), Learning to Coordinate Control Polices of Hybrid Systems, Proc. of American Control Conf., pp.31–35.Google Scholar
  9. 9.
    J.Lu, L.Liao, A.Nerode and J.H.Taylor(1993), Optimal Control of Systems with Continuous and Discrete state, Proc. of the 32th Conf. Decision and Control, pp. 2292–2297.Google Scholar
  10. 10.
    P. Peleties and R. DeCarlo(1989), A Modeling Strategy with Event Structures for Hybrid Systems, Proc. of the 28th Conf. Decision and Control, pp.1308–1313.Google Scholar
  11. 11.
    J.A. Stiver and P.J. Antsaklis(1992), Modeling and analysis of hybrid control Systems, Proc. of the 31th Conf. Decision and Control, pp.3748–3751.Google Scholar
  12. 12.
    J.A. Stiver and P.J. Antsaklis(1993), On the Controllability of Hybrid Control Systems, Proc. of the 32th Conf. Decision and Control, pp.294–299.Google Scholar
  13. 13.
    P.J. Ramadge and W.M. Wonham(1987), Supervisory Control of A Class of Discrete Event Processes, SIAM J. Control and Optimization, Vol.25, No.1, pp.206–230.CrossRefGoogle Scholar
  14. 14.
    W.M. Wonham and P.J. Ramadge(1987), On the supremal controllable sublanguage of a given language, SIAM J. Control and Optimization, Vol.25, No.3, pp.637–659CrossRefGoogle Scholar
  15. 15.
    X. Feng, K.A. Loparo, Y. Ji, H.J. Chizeck(1992), Stochastic Stability Properties of Jump linear Systems, IEEE Tr. on AC, Vol. 37, No. 1, pp 38–53.Google Scholar
  16. 16.
    R. Brockett(1994), Language Driven Hybrid Systems, Proc. of the 33rd Conf. Decision and Control, pp.4210–4214.Google Scholar
  17. 17.
    B. Lennartson, B. Egardt, and M. Tittus(1994), Hybrid Systems in Process Conrol, Proc. of the 33rd Conf. Decision and Control, pp.3587–3592.Google Scholar
  18. 18.
    J.A. Stiver, P.J. Antsaklis, and M.D. Lemmon(1994), Digital Control from a Hybrid Perspective, Proc. of the 33rd Conf. Decision and Control, pp.4241–4246.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Hong Seong Park
    • 1
  • Young Sin Kim
    • 2
  • Wook Hyun Kwon
    • 2
  • Sang Jeong Lee
    • 3
  1. 1.Dept. of Control and Instrumentation Engr.Kangwon National UniversityKangwon-doKorea
  2. 2.Dept. of Control and Instrumentation Engr.Seoul National UniversitySeoulKorea
  3. 3.Dept. of Electronics EngineeringChungnam National UniversityDaejeonKorea

Personalised recommendations