Browsing by Author "Kliemann, Wolfgang"

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    Near invariance and local transience for random diffeomorphisms
    (TAYLOR & FRANCIS LTD, 2010) Colonius, Fritz; Homburg, Ale Jan; Kliemann, Wolfgang
    For random diffeomorphisms depending on a parameter, nearly invariant sets are described via an associated deterministic control system. Conditions are provided guaranteeing that the system leaves the support of an invariant measure under small perturbations of the parameter and estimates for the exit times are given.
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    Stability of linear stochastic systems via Lyapunov exponents and applications to power systems
    (ELSEVIER SCIENCE INC, 2012) Verdejo, Humberto; Vargas, Luis; Kliemann, Wolfgang
    This paper studies linear systems under sustained random perturbations. The stochastic perturbation model is given by a bounded Markov diffusion process, as it appears, e. g., in the description of load or generation uncertainties of power systems. For such systems, the Lyapunov exponents describe necessary and sufficient conditions for almost sure asymptotic stability. The paper presents several numerical methods for the computation of Lyapunov exponents and applies this methodology to linear oscillators in dimension 2 and 3, and to a one machine - infinite bus electric power system. (C) 2012 Elsevier Inc. All rights reserved.