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On the Stabilizability of Control Constrained Linear Systems

  • Mikhail Krastanov
  • Vladimir Veliov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2542)

Abstract

We study the problem of stabilization of time-invariant linear systems with controls which are constrained in a cone. Under small-time local controllability conditions we propose a simple construction of a Lipschitz piecewise linear stabilizing feedback. Moreover, we show that the stabilizing feedback can be chosen in such a way that the number of switchings from one linear form to another, that may occur along a trajectory of the closed-loop system, is uniformly bounded.

Keywords

Convex Cone Linear Feedback Closed Convex Cone Admissible Trajectory Polyhedral Convex Cone 
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.

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References

  1. 1.
    Ackermann, J.: Sampled-Data Control Systems. Springer-Verlag, Berlin (1985)Google Scholar
  2. 2.
    Ackermann, J., Utkin, V.: Sliding Mode Control Design Based on Ackermann’s Formula. IEEE Transactions on Automatic Control, 43 (1998) No. 2, 234–237.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bianchini, R.M.: Instant Controllability of Linear Autonomous Systems. J. Optimiz. Theory Appl., 39 (1983) 237–250.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Smirnov, G.V.: Stabilization by Constrained Controls. SIAM J. Control and Optimization, 34 (1996) No 5 1616–1649.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Sontag, E., Yang, Y., Sussmann, H.: A General Result on the Stabilization of Linear Systems Using Bounded Controls. IEEE Transactions on Automatic Control, 39 (1994) No. 12 2411–2425.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Sussmann, H.: Small-time Local Controllability and Continuity of the Optimal Time Function for Linear Systems. J. Optimization Theory Appl., 53 (1987) 281–296.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Veliov, V.: On the Controllability of Control Constrained Systems.Mathematica Balkanica, New series, 2 (1988) No. 2–3 147–155.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Yang, Y., Sussmann, H.: On the Stabilizability of Multiple Integrators by Means of Bounded Feedback Controls. Proc. of the 30-th IEEE Conference on Decision and Control, Brighton, UK, Dec. 1991, IEEE Publications, New York, 70–72.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Mikhail Krastanov
    • 1
  • Vladimir Veliov
    • 1
    • 2
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofia
  2. 2.Institute for Econometrics, Operations Research and Systems TheoryVienna University of TechnologyViennaAustria

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