ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1990 · 84 citations · 10 references
Natural SciencesMathematicsDynamical SystemsStochastic ProcessesSystem DynamicsControl TheoryLyapunov ExponentsStabilityStability TheoryStochastic Differential EquationsStochastic StabilityExponential GrowthGrowth RatesLyapunov FunctionsLyapunov StabilityLyapunov Stability AnalysisStochastic Control StabilityStochastic Lyapunov FunctionsWhite Noise
Abstract Given a d × d matrix A and a d × k matrix B. We investigate how the stability behavior of ẋ = (A + BG(t)) × can be improved by a k × d matrix‐valued white noise process G(t). The analysis is based on the theory of Lyapunov exponents (exponential growth rates) and uses an averaging principle. It generalizes a result by the author and co‐workers for the case B = identity, in which the top Lyapunov exponent can be brought arbitrarily close to trace A/d by cleverly choosing G(t).
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