Abstract
The method of vector Lyapunov functions to determine stability in dynamical systems requires that the comparison system be quasimonotone nondecreasing with respect to a cone contained in the nonnegative orthant. For linear comparison systems in Rn with real spectra, Heikkilä solved the problem for n = 2 and gave necessary conditions for n > 2. We previously showed a sufficient condition for n > 2, and here, for systems with complex eigenvalues, we give conditions for which the problem reduces to the nonnegative inverse eigenvalue problem.
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