In this brief note, we study the problem of asymptotic behavior solutions for non-resonant, singularly perturbed linear Neumann boundary value problems εy″+ky=f(t), y′(a)=0, y′(b)=0, k>0, with an indication possible extension to more complex cases. Our approach is based on analysis integral equation associated problem.

In this letter, we consider the ultimate boundedness of the singularly perturbed system with measurement noise. The composite controller is commonly used to regulate the singularly perturbed system. However, in the presence of measurement noise, the composite controller does not guarantee the ultimate boundedness of the singularly perturbed system. Thus, we propose the modified composite contro...

A class of quasilinear singularly perturbed problems with boundary perturbation is considered. Under suitable conditions, using theory of differential inequalities we studied the asymptotic behavior of the solution for the boundary value problem.

Abstract In this paper, we have developed a fifth order compact difference method for a class of singularly perturbed singular two-point boundary value problems. To avoid the singularity at zero a terminal boundary condition in the implicit form is derived. Using this condition as one of the boundary condition we solve the singularly perturbed singular two-point boundary value problem by the fi...

This paper investigates the stability problem of a class of discrete-time singularly perturbed Tagagi–Sugeno (T-S) fuzzy models. Stability conditions of reduced slow models, based on the use of Borne and Gentina practical stability criterion and matrices in the arrow form, are developed and compared with those concerning the initial singularly perturbed T-S system. The obtained results are prac...

In this brief, we study the near-optimal Kalman filtering problem for multiparameter singularly perturbed system (MSPS). The attention is focused on the design of the near-optimal Kalman filters. It is shown that the resulting filters in fact remove ill-conditioning of the original full-order singularly perturbed Kalman filters. In addition the resulting filters can be used compared with the pr...

We consider singularly perturbed differential systems in cases where the standard theory to establish a slow integral manifold existence does not work. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. Applying transformations we reduce the original singularly perturbed problem to a re...

The problem of state-feedback control design for a class of singularly perturbed systems with time delays and norm-bounded nonlinear uncertainties is studied in this paper. The system under consideration considers discrete delays in both slow and fast dynamics and norm-bounded nonlinear uncertainties. It is shown that the control gains are obtained to guarantee the stability of the closed-loop ...