We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the highest possible relative accuracy.

This paper is concerned with the problem of designing a robust adaptive controller for flexible joint robots (FJR). Under the assumption of weak joint elasticity, FJR is firstly modeled and converted into singular perturbation form. The control law consists of a FAT-based adaptive control strategy and a simple correction term. The first term of the controller is used to stability of the slow dy...

A numerical method for a singular perturbation problem with a turning point is considered. The method uses non-equidistant discretization meshes. The first order accuracy, uniform in the perturbation parameter is proved in the discrete L1 norm.

We consider a singular elliptic perturbation of a Hammerstein integral equation with singular nonlinear term at the origin. The compactness of the solutions to the perturbed problem and, hence, the existence of a positive solution for the integral equation are proved. Moreover, these results are applied to nonlinear singular homogeneous Dirichlet problems.

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

The speech enhancement techniques are often employed to improve the quality and intelligibility of the noisy speech signals. This paper discusses a novel technique for speech enhancement which is based on Singular Value Decomposition. This implementation utilizes a Genetic Algorithm based optimization method for reducing the effects of environmental noises from the singular vectors as well as t...

In this paper, laminar condensation on a spherical drop in a forced flow is investigated. The drop experiences a strong, radial, condensation-induced velocity while undergoing slow translation. In view of the high condensation velocity, the flow field, although the drop experiences slow translation, is not in the Stokes-flow regime. The drop environment is assumed to consist of a mixture of sat...

The problem of output regulation for nonlinear control systems with guaranteed transient performances in the presence of uncertainties is discussed, where the nonlinear systems are nonaffine in the control. The fast dynamical controller with the highest output derivative in feedback loop is used, where the controller is proper and can be implemented without ideal differentiation. Two-time-scale...

The paper treats a question of proportional-integral-derivative (PID) controller design for aircraft pitch attitude in the presence of uncertain aerodynamics. The presented design methodology guarantees desired pitch attitude transient performance indices by inducing of two-time-scale motions in the closed-loop system where the controller dynamics is a singular perturbation with respect to the ...

* Firstly, we wish to find a lower bound, i.e. the functional I(φ) such that for every family {φε}ε>0, satisfying φε → φ as ε → 0 , we have limε→0+ Iε(φε) ≥ I(φ). ** Secondly, we wish to find an upper bound, i.e. the functional I(φ) such that there exists the family {ψε}ε>0, satisfying ψε → φ as ε → 0 , and we have limε→0+ Iε(ψε) ≤ I(φ). *** If we obtain I(φ) = I(φ) := I(φ), then I(φ) will be t...