Stabilizing Second-Order Linear Dynamic Systems Via Hybrid Output Feedback Controls

  • Liguo Zhang
  • Yangzhou Chen
  • Pingyuan Cui
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)


This paper considers the open problem whether there exists a finite-state hybrid output feedback control to asymptotically stabilize a second-order linear dynamic system. More precisely, for second-order linear time-invariant systems which are not stabilizable via a single static output feedback, we find two different output feedback gains and a switching law orchestrating the feedback gains such that the closed-loop system is asymptotically stable.


Output Feedback Static Output Feedback Switch Linear System Piecewise Linear System Control System Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Syrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K.: Static output feedback: a survey. Automatica 33, 125–137 (1997)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Artstein, Z.: Examples of stabilization with hybrid feedback. In: Alur, R., et al. (eds.) Hybrid Systems III: Verification and Control, pp. 173–185 (1996)Google Scholar
  3. 3.
    Liberzon, D.: Stabilizing a linear system with finite-state hybrid output feedback. In: Proceedings of the 7th IEEE Mediterranean Conference on Control and Automation, pp. 176–183 (1999)Google Scholar
  4. 4.
    Liberzon, D., Morse, A.S.: Basic problems in stability and design of switched systems. IEEE Control Systems Magazine 19, 59–70 (1999)CrossRefGoogle Scholar
  5. 5.
    Hu, B., Zhai, G., Michel, A.N.: Hybrid output feedback stabilization of two-dimensional linear control systems. In: Proceedings of the 2000 American Control Conference, pp. 2184–2188 (2000)Google Scholar
  6. 6.
    Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Control 43, 475–482 (1998)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    DeCarlo, R., Branicky, M., Pettersson, S., Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE 88, 1069–1082 (2000)CrossRefGoogle Scholar
  8. 8.
    Johansson, M., Rantzer, A.: Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Trans. Automat. Control 43, 555–559 (1998)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Michel, A.N.: Recent trends in the stability analysis of hybrid dynamical systems. IEEE Trans. Circuit and Systems-I: Fundamental Theory and Applications 45, 120–134 (1999)CrossRefGoogle Scholar
  10. 10.
    Morse, A.S.: Control using logic-based switching. In: Isidori, A. (ed.) Trends in Control: a European Perspective, pp. 69–113. Springer, Berlin (1995)Google Scholar
  11. 11.
    Peleties, P., DeCarlo, R.: Asymptotic stability of m-switched systems using Lyapunov-like functions. In: Proceedings of the 1991 American Control Conference, pp. 1679–1684 (1991)Google Scholar
  12. 12.
    Litsyn, E., Nepomnyashchikh, Y.V., Ponosov, A.: Stabilization of linear differential systems via hybrid feedback controls. SIAM J. Control Optim. 38, 1468–1480 (2000)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Xu, X., Antsaklis, P.J.: Design of stabilizing control laws for second-order switched systems. In: Proceedings of the 14th IFAC World Congress, vol. C, pp. 181–186 (1999)Google Scholar
  14. 14.
    Xu, X., Antsaklis, P.J.: Stabilization of second-order LTI switched systems. Int. J. Control 73, 1261–1279 (2000)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Sastry, S.: Nonlinear Systems. Springer, New York (1999)MATHGoogle Scholar
  16. 16.
    Zhang, L., Chen, Y., Cui, P.: Stabilization of a Class of Switched Linear Systems, Nonlinear Analysis: Theory, Methods and Applications. Special Issue on Hybrid Systems and Applications 62, 1527–1535 (2005)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Liguo Zhang
    • 1
  • Yangzhou Chen
    • 1
  • Pingyuan Cui
    • 1
  1. 1.School of Electronic and Control EngineeringBeijing University of TechnologyBeijingChina

Personalised recommendations