Abstract
For a linear impulsive differential equation, we give a complete characterization of the existence of a nonuniform exponential contraction in terms of quadratic Lyapunov functions and of the operators defining them. This corresponds to consider a nonuniform exponential stability of the dynamics, which is typical for example in the context of ergodic theory. As an application, we use this characterization to establish in a very simple manner the robustness property of a nonuniform exponential contraction under sufficiently small linear perturbations. In addition, we obtain versions of the robustness property for perturbations of the jumping times and of a strong nonuniform exponential contraction. The latter corresponds to consider not only an upper bound for the dynamics but also a lower bound.
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Supported by FCT/Portugal through UID/MAT/04459/2013.
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Barreira, L., Valls, C. Robustness for Stable Impulsive Equations via Quadratic Lyapunov Functions. Milan J. Math. 84, 63–89 (2016). https://doi.org/10.1007/s00032-016-0251-8
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DOI: https://doi.org/10.1007/s00032-016-0251-8