The quasimonotonicity of linear differential systems — the complex spectrum

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.

Keywords:

• Vector Lyapunov functions
• Cones
• Quasimonotonicity
• Dynamical systems

AMS Classifications:

• 15A48
• 34D20

^*Corresponding author. [email protected]

^† [email protected]

^*Corresponding author. [email protected]

^† [email protected]

Notes

^*Corresponding author. [email protected]

^† [email protected]