The quasimonotonicity of linear differential systems - the complex spectrum

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, Heikkila solved the problem for n = 2 and gave necessary conditions for n> 2. We previously showed a sucient 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.