A procedure for the construction of robust, upper bounds for the error in the finite element approximation of singularly perturbed reaction diffusion problems was presented in [2] which entailed the solution of an infinite dimensional local boundary value problem. It is not possible to solve this problem exactly and this fact was recognised in the above work where it was indicated that the limi...

Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi timescale systems. In this paper a contraction theory based framework is proposed for stabilization of singularly perturbed systems. The primary objective is to design a feedback controller to achieve bounded tracking error for both standard an...

By using the method of Newton diagrams and asymptotic methods theory differential equations, we construct asymptotics general solutions to linear homogeneous singularly perturbed systems equations obtained in investigation some problems stability circular cylindrical shells.

In the case of regular boundary value problems, effective numerical methods based on domain decomposition are well known (see, for example, [1, 2] and the list of references there). Such methods allows us to reduce the solution of complicated problems with several characteristic scales to solving simplified problems on simpler subdomains and, in particular, to implement parallel computations. E...

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of uncertain Markovian jump nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model with Markovian jumps. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear singularly perturbed systems to have an ...

A numerical method based on parametric spline with adaptive parameter is given for the secondorder singularly perturbed two-point boundary value problems of the form 0 1 ( ) ( ) ( ); ( ) ; ( ) y p x y q x y r x y a y b           The derived method is second-order and fourth-order convergence depending on the choice of the two parameters  and  . Error analysis of a method is briefly...

This paper presents the closed-loop composite control of singularly perturbed bilinear systems with a quadratic performance criterion, using successive Galerkin approximation(SGA). The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time and fast-time scale by the singular perturbation theory, and we obtain feedback control laws from each subsystem using SGA. We...

In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. ...

In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. ...