this paper presents some analyses about the robust practical stability of a class of nonlinear affine systems in the presence of non-vanishing perturbations based on the passivity concept. the given analyses confirm the robust passivity property of the perturbed nonlinear systems in a certain region. moreover, robust control laws are designed to guarantee the practical stability of the perturbe...

This paper presents some analyses about the robust practical stability of a class of nonlinear affine systems in the presence of non-vanishing perturbations based on the passivity concept. The given analyses confirm the robust passivity property of the perturbed nonlinear systems in a certain region. Moreover, robust control laws are designed to guarantee the practical stability of the perturbe...

We establish basic local existence as well as a stability result concerning small perturbations of the Catenoid minimal surface in R3 under hyperbolic vanishing mean curvature flow.

We investigate the cosmological perturbations of the brane-induced (Dvali-GabadadzePorrati) model which exhibits a van Dam-Veltman-Zakharov (vDVZ) discontinuity when linearized over a Minkowski background. We show that the linear brane scalar cosmological perturbations over an arbitrary Friedmann-Lemâıtre-Robertson-Walker (FLRW) spacetime have a well defined limit when the radius of transition ...

We study integrable lattice equations and their perturbations over finite fields. We write these equations in projective coordinates and assign boundary values along axes in the first quadrant. We propose some growth diagnostics over finite fields that can often distinguish between integrable equations and their non-integrable perturbations. We also discuss the limitations of the diagnostic. Fi...

The conditions for the existence of negative-energy perturbations (which could be nonlinearly unstable and cause anomalous transport) are investigated in the framework of linearized collisionless Maxwell-drift kinetic theory for the case of equilibria of magnetically confined, circularly cylindrical plasmas and vanishing initial field perturbations. For wave vectors with a non-vanishing compone...

We study the Gaussian semiclassical soliton ensemble, a collection of multisoliton solutions of the focusing nonlinear Schrödinger equation. The ensemble is generated by adding a particular asymptotically vanishing sequence of perturbations to Gaussian initial data. Recent results [Lee, Lyng, & Vankova (2012)] suggest that, remarkably, these perturbations—interlaced as they are with the integra...

In the present paper, we study robustness properties of a class of digital feedback control systems with time-varying sampling periods consisting of an interconnection of a continuous-time nonlinear plant (described by systems of rst-order ordinary diierential equations), a nonlinear digital controller (described by systems of rst-order ordinary diierence equations), and appropriate interface e...

We express the total equation of state parameter of a spatially flat FriedmanRobertson-Walker universe in terms of derivatives of the red-shift dependent spinweighted angular moments of the two-point correlation function of the three dimensional cosmic shear. We first express the total equation of state parameter in terms of the growing mode of the gauge invariant metric perturbation in the con...