This paper is concerned with a class of singularly perturbed systems of two conservation laws. A small perturbation parameter is introduced in the dynamics and the boundary conditions. By setting the perturbation parameter to zero, the singularly perturbed system of conservation laws can be treated as two subsystems of one conservation law: the reduced system and the boundary-layer system. The ...

The derivatives of the solution of singularly perturbed diierential equations become unbounded as the singular perturbation parameter " tends to zero. Therefore to approximate such derivatives, it is required to scale the derivatives in such a way that they are of order one for all values of the perturbation parameter. In practice , derivatives are related to the ux or drag and, hence, it is de...

Abstract – In this paper we present a unified approach for optimal control and filtering of linear continuous-time singularly perturbed linear systems that facilitates complete and exact decomposition of optimal control and filtering tasks into pure-slow and pure-fast time scales. The presented methodology eliminates numerical ill-conditioning of the original singularly perturbed problems, intr...

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 ...

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...

 This paper studies the characterization of the stability boundary (the topological boundary of stability region) of nonlinear autonomous singularly perturbed dynamical systems. In particular, a relationship between the stability boundary of the singularly perturbed system and the stability boundary and stability region of the slow and fast systems is investigated. Conditions, in terms of loca...