A novel criterion for global incremental stability of dynamical systems

TL;DR

This paper introduces new sufficient conditions for global incremental stability of nonlinear dynamical systems, using a logarithmic norm approach that generalizes existing criteria and applies even when the origin is not an equilibrium.

Contribution

It presents an alternative method for assessing global incremental stability via logarithmic norms, extending the Demidovich criterion and analyzing convergence without requiring the origin to be an equilibrium.

Findings

Provided sufficient conditions for global uniform exponential stability.

Generalized Demidovich criterion for broader classes of systems.

Validated the theory with a simulation experiment.

Abstract

In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability (GIS) of the systems. We provide here an alternative approach for assessment of GIS in terms of logarithmic norm under which the stability becomes a topological notion and also generalize both horizontally and vertically the well-known Demidovich criterion for GIS of dynamical systems. Convergence of all solutions to the origin x=0, which is not assumed to be an equilibrium state of system, is also analyzed. Theory is illustrated by a simulation experiment.