in this paper robust pid control of fully-constrained cable driven parallel manipulators with elastic cables is studied in detail. in dynamic analysis, it is assumed that the dominant dynamics of cable can be approximated by linear axial spring. to develop the idea of control for cable robots with elastic cables, a robust pid control for cable driven robots with ideal rigid cables is firstly de...

This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter ǫ, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable vector function b. The equation being supplemented with Neumann boundary conditions, the limit ǫ→0 is demonstrated to be a singular perturbation of the original diffusi...

The state feedback H1 control problem for standard discrete-time singularly perturbed systems with polytopic uncertainties is considered. Two methods for designing H1 controllers are given in terms of solutions to a set of linear matrix inequalities, where one of them is with the consideration of improving the upper bound of singular perturbation parameter e. Moreover, a method of evaluating th...

A singularly perturbed linear convection-diffusion problem for heat transfer in two dimensions with a parabolic boundary layer is solved numerically. The numerical method consists of a special piecewise uniform mesh condensing in a neighbourhood of the parabolic layer and a standard finite difference operator satisfying a discrete maximum principle. The numerical computations demonstrate numeri...

Abstract. In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with n independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002), 313–322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singul...

This paper addresses the H1 control problem via slow state variables feedback for discretetime fuzzy singularly perturbed systems. At first, a method of evaluating the upper bound of singular perturbation parameter with meeting a prescribed H1 performance bound requirement is given. Subsequently, two methods for designing H1 controllers via slow state variables feedback are presented in terms o...

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...

A survey is presented describing the application of singular perturbation techniques to queueing systems. The goal is to compute performance measures by constructing approximate solutions to specific problems involving either the Kolmogorov forward or backward equation which contain a small parameter. These techniques are particularly useful on problems for which exact solutions are not availab...

Certain singularly perturbed partial diierential equations exhibit a phenomenon known as dynamic metastability, whereby the solution evolves on an asymptotically exponentially long time interval as the singular perturbation parameter tends to zero. This article illustrates a technique to analyze metastable behavior for a range of problems in multi-dimensional domains. The problems considered in...

Various variants of Schwarz methods for a singularly perturbed two dimensional stationary convection-diffusion problem are constructed and analysed. The iteration counts, the errors in the discrete solutions and the convergence behaviour of the numerical solutions are analysed in terms of their dependence on the singular perturbation parameter of the Schwarz methods. Conditions for the methods ...