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A converse Lyapunov theorem for switched DAEs

  1. Stephan Trenn1,*,
  2. Fabian Wirth2

Article first published online: 3 DEC 2012

DOI: 10.1002/pamm.201210381

Issue

PAMM

PAMM

Special Issue: 83rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Darmstadt 2012; Editors: H.-D. Alber, N. Kraynyukova and C. Tropea

Volume 12, Issue 1, pages 789–792, December 2012

Additional Information

How to Cite

Trenn, S. and Wirth, F. (2012), A converse Lyapunov theorem for switched DAEs. Proc. Appl. Math. Mech., 12: 789–792. doi: 10.1002/pamm.201210381

Author Information

  1. 1

    Department of Mathematics, TU Kaiserslautern, Erwin Schrödinger Str. Geb. 48, 67663 Kaiserslautern, Germany

  2. 2

    Institute for Mathematics, University of Würzburg, Emil-Fischer-Str. 40, 97074 Würzburg, Germany

*Department of Mathematics, TU Kaiserslautern, Erwin Schrödinger Str. Geb. 48, 67663 Kaiserslautern, Germany

Publication History

  1. Issue published online: 3 DEC 2012
  2. Article first published online: 3 DEC 2012

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References

  • [1]
    V. S. Kozyakin. Algebraic unsolvability of problem of absolute stability of desynchronized systems. Autom. Rem. Control, 51(6):754–759, 1990.
  • [2]
    Daniel Liberzon and Stephan Trenn. Switched nonlinear differential algebraic equations: Solution theory, Lyapunov functions, and stability. Automatica, 48(5):954–963, May 2012.
  • [3]
    Yuandan Lin, Eduardo D. Sontag, and Yuan Wang. A smooth converse Lyapunov theorem for robust stability. SIAM J. Control Optim., 34(1):124–160, 1996.
  • [4]
    Aneel Tanwani and Stephan Trenn. On observability of switched differential-algebraic equations. In Proc. 49th IEEE Conf. Decis. Control, Atlanta, USA, pages 5656–5661, 2010.
  • [5]
    Fabian R. Wirth. The generalized spectral radius and extremal norms. Lin. Alg. Appl., 342:17–40, 2002.
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