This paper concerned with a model reduction of infinite dimensional systems by using the singular perturbation approximation. The system considered is that of the exponentially stable linear system with bounded and finite-rank input and output operators such that the balanced realization can be performed on the system. Furthermore, the singular perturbation method is applied to reduce the order...

Poisson-Nernst-Planck (PNP) systems are considered in the case of vanishing permanent charge. A detailed case study, based on natural categories described by system boundary conditions and flux, is carried out via simulation and singular perturbation analysis. Our results confirm the rich structure inherent in these systems. A natural quantity, the quotient of the Debye and characteristic lengt...

We show that stationary statistical properties for uniformly dissipative dynamical systems are upper semi-continuous under regular perturbation and a special type of singular perturbation in time of relaxation type. The results presented are applicable to many physical systems such as the singular limit of infinite Prandtl-Darcy number in the Darcy-Boussinesq system for convection in porous med...

A singularly perturbed model is proposed for a system comprised of a PEM Fuel Cell(PEM-FC) with Natural Gas Hydrogen Reformer (NG-HR). This eighteenth order system is decomposedinto slow and fast lower order subsystems using singular perturbation techniques that provides tools forseparation and order reduction. Then, three different types of controllers, namely an optimal full-order,a near-opti...

In this paper we study the singular perturbation of ∫ (1−|∇u|2)2 by ε2|∇2u|2. This problem, which could be thought as the natural second order version of the classical singular perturbation of the potential energy ∫ (1 − u2)2 by ε2|∇u|2, leads, as in the first order case, to energy concentration effects on hypersurfaces. In the two dimensional case we study the natural domain for the limiting e...

It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundary-value singular perturbation problem admits a decomposition into a regular part and a finite linear combination of explicit singular functions. Taking into acco...

A new general bilinear relationship is found between continuous and discrete generalized singular perturbation (GSP) reduced-order models. This result is applied to the problem of deriving discrete analogs of continuous singular perturbation and direct truncation model reduction and leads to a new definition of discrete "Nyquist" model reduction. Also, "unit circle" bilinear transformations are...

For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the normal form method, center manifold theory, and the renormalization group method are well known. It is shown that all of the solutions of the reduced equatio...

In this paper, the differential transform method is used to find approximate analytical and numerical solutions of singular perturbation problems. The principle of the method is briefly introduced and then applied for solving two mathematical models of stiff initial value singular perturbation problems. The results are then compared with the exact solutions to demonstrate the reliability and ef...

The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channel’s charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singul...