Exponential stabilisation of non-standard nonlinear singularly perturbed system

Abstract

The authors investigate the exponential stability of non-standard nonlinear singularly perturbed system via the Lyapunov stability technique. Using two standard singularly perturbed systems separated from the nonstandard system, the authors analyse the exponential stability of the non-standard nonlinear singularly perturbed system. Based on the stability analysis for the general singularly perturbed system with non-separate slow-fast dynamics, the stabilising controller is designed.