Search results for "Nonlinear system"

Observer-based finite-time control for discrete fuzzy jump nonlinear systems with time delays

2013

This paper investigates the problem of observer-based finite-time H∞ control for a family of discrete jump nonlinear systems with time delays represented by Takagi-Sugeno (T-S) model. The main contribution of this paper is to design an observer-based finite-time H∞ controller such that the resulting closed-loop system is stochastic finite-time bounded and satisfies a prescribed H∞ disturbance attenuation level over the given finite-time interval. Sufficient criteria on stochastic finite-time H∞ stabilization via observer-based fuzzy state feedback are provided for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. A simulati…

Finite-time stabilization for discrete fuzzy jump nonlinear systems with time delays

2013

This paper is concerned with the problem of finite-time H∞ control for a class of discrete-time Markovian jump nonlinear systems with time delays represented by Takagi-Sugeno (T-S) model. First, by using fuzzy stochastic Lyapunov-Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastic finite-time bounded and satisfies a prescribed H∞ disturbance attenuation level in a given finite-time interval. Second, sufficient criteria on stochastic finite-time H∞ stabilization via fuzzy state feedback are provided, and the fuzzy state feedback controller is designed by solving an optimization problem in terms of linear matrix inequalitie…

Probabilistic response of nonlinear systems via PI: normal, Poissonian and combined white noises

2009

Nonlinear calculations of the energy loss of slow ions in an electron gas

1986

Abstract The stopping power of an electron gas for slow ons was calculated based on nonlinear, density-functional methods. These new theoretical results show substatnial increases in stopping powers for protons compared to calculations based on linear theory and provide a good qualitative description of the Z1-oscillations found in experimental data.

Multiplicity distributions and long range rapidity correlations

2010

The physics of the initial conditions of heavy ion collisions is dominated by the nonlinear gluonic interactions of QCD. These lead to the concepts of parton saturation and the Color Glass Condensate (CGC). We discuss recent progress in calculating multi-gluon correlations in this framework, prompted by the observation that these correlations are in fact easier to compute in a dense system (nucleus-nucleus) than a dilute one (proton-proton).

Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme

2017

This is the second part of our error analysis of the stabilized Lagrange-Galerkin scheme applied to the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear elements, which leads to an efficient computation with a small number of degrees of freedom especially in three space dimensions. In this paper, Part II, we apply a semi-implicit time discretization which yields the linear scheme. We concentrate on the diffusive viscoelastic model, i.e. in the constitutive equation for time evolution of the conformation tensor a diffusive effect is included. Under mild stability condi…

A note on the uniqueness and attractive behavior of solutions for nonlinear Volterra equations

2001

In this paper we prove that positive solutions of some nonlinear Volterra integral equations must be locally bounded and global attractors of positive functions. These results complete previous results about the existence and uniqueness of solutions and their attractive behavior.

Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour

2019

Abstract The numerical solution of nonlinear convection-diffusion equations with nonlocal flux by explicit finite difference methods is costly due to the local spatial convolution within the convective numerical flux and the disadvantageous Courant-Friedrichs-Lewy (CFL) condition caused by the diffusion term. More efficient numerical methods are obtained by applying second-order implicit-explicit (IMEX) Runge-Kutta time discretizations to an available explicit scheme for such models in Carrillo et al. (2015) [13] . The resulting IMEX-RK methods require solving nonlinear algebraic systems in every time step. It is proven, for a general number of space dimensions, that this method is well def…

The local boundedness of solutions for a class of degenerate nonlinear elliptic higher-order equations withL1-data

2008

We prove local boundedness of solutions for a class of degenerate nonlinear elliptic higher-order equations with L(1)-data.

On the implementation of weno schemes for a class of polydisperse sedimentation models

2011

The sedimentation of a polydisperse suspension of small rigid spheres of the same density, but which belong to a finite number of species (size classes), can be described by a spatially one-dimensional system of first-order, nonlinear, strongly coupled conservation laws. The unknowns are the volume fractions (concentrations) of each species as functions of depth and time. Typical solutions, e.g. for batch settling in a column, include discontinuities (kinematic shocks) separating areas of different composition. The accurate numerical approximation of these solutions is a challenge since closed-form eigenvalues and eigenvectors of the flux Jacobian are usually not available, and the characte…