The quasimonotonicity of linear differential systems

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 with real eigenvalues, we show some necessary and sufficient conditions for such cones to exist, and we show a method to construct such cones.

Keywords:

• Vector Lyapunov functions
• cones
• quasimonotonicity
• dynamical systems