TY - JOUR
T1 - Switched nonlinear differential algebraic equations
T2 - Solution theory, Lyapunov functions, and stability
AU - Liberzon, Daniel
AU - Trenn, Stephan
N1 - Funding Information:
This work was supported by NSF grants CNS-0614993 , ECCS-0821153 and DFG grant Wi1458/10-1 . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Maurice Heemels under the direction of Editor Andrew R. Teel (Nonlinear Systems and Control).
PY - 2012/5
Y1 - 2012/5
N2 - We study switched nonlinear differential algebraic equations (DAEs) with respect to existence and nature of solutions as well as stability. We utilize piecewise-smooth distributions introduced in earlier work for linear switched DAEs to establish a solution framework for switched nonlinear DAEs. In particular, we allow induced jumps in the solutions. To study stability, we first generalize Lyapunov's direct method to non-switched DAEs and afterwards obtain Lyapunov criteria for asymptotic stability of switched DAEs. Developing appropriate generalizations of the concepts of a common Lyapunov function and multiple Lyapunov functions for DAEs, we derive sufficient conditions for asymptotic stability under arbitrary switching and under sufficiently slow average dwell-time switching, respectively.
AB - We study switched nonlinear differential algebraic equations (DAEs) with respect to existence and nature of solutions as well as stability. We utilize piecewise-smooth distributions introduced in earlier work for linear switched DAEs to establish a solution framework for switched nonlinear DAEs. In particular, we allow induced jumps in the solutions. To study stability, we first generalize Lyapunov's direct method to non-switched DAEs and afterwards obtain Lyapunov criteria for asymptotic stability of switched DAEs. Developing appropriate generalizations of the concepts of a common Lyapunov function and multiple Lyapunov functions for DAEs, we derive sufficient conditions for asymptotic stability under arbitrary switching and under sufficiently slow average dwell-time switching, respectively.
KW - Asymptotic stability
KW - Lyapunov functions
KW - Nonlinear differential algebraic equations
KW - Piecewise-smooth distributions
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U2 - 10.1016/j.automatica.2012.02.041
DO - 10.1016/j.automatica.2012.02.041
M3 - Article
AN - SCOPUS:84859755770
SN - 0005-1098
VL - 48
SP - 954
EP - 963
JO - Automatica
JF - Automatica
IS - 5
ER -