<p>We explicitly compute the maximal Lyapunov exponent for a switched system on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathrm{SL}_{2}(\mathbb{R})\)</EquationSource> </InlineEquation> and the corresponding switching function which realizes the maximal exponent. This computation is reduced to the characterization of optimal trajectories for an optimal control problem on the Lie group.</p>

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Lyapunov Exponents of Linear Switched Systems

  • Andrei A. Agrachev,
  • Michele Motta

摘要

We explicitly compute the maximal Lyapunov exponent for a switched system on \(\mathrm{SL}_{2}(\mathbb{R})\) and the corresponding switching function which realizes the maximal exponent. This computation is reduced to the characterization of optimal trajectories for an optimal control problem on the Lie group.