Passivity analysis of singularly perturbed systems with nonlinear uncertainties

This paper considers the problem of passivity analysis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameter, a new method for estimating the allowable upper bound of the singular perturbation parameter is proposed, under which the singularly perturbed system is passive when the singular perturbation parameter is lower than this upper bound. The proposed method is shown to be less conservative than the existing method because the adopted storage function is more general. Finally, a RLC circuit is presented to illustrate the advantages and effectiveness of the proposed method.