Passive Control and ε -Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities

This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameter ε , a new method is proposed to estimate the ε -bound, such that the system is passive when the singular perturbation parameter is lower than the ε -bound. Furthermore, a controller design method is proposed to achieve a predefined ε -bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.