Robust stability of nonlinear singularly perturbed system with uncertainties

The singularly perturbed system is easily analysed by two time-scale systems, each of which with a lower dimension than the original system. However, if uncertainties are added, then the analysis is very difficult because uncertainties change the slow manifold, the boundary layer model and the reduced model of the nominal system. Robust stability analysis of nonlinear singularly perturbed systems with vanishing uncertainties, of which the upper norm bounds only are available, is presented. The stability condition, under which the zero state equilibrium of the singularly perturbed system is exponentially stable for the sufficiently small perturbation parameter ε, is found and a stabilising controller is proposed.