Search results for "Linear system"

A taxonomy for wavelet neural networks applied to nonlinear modelling

2008

This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.

Edge detection insensitive to changes of illumination in the image

2010

In this paper we present new edge detection algorithms which are motivated by recent developments on edge-adapted reconstruction techniques [F. Arandiga, A. Cohen, R. Donat, N. Dyn, B. Matei, Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques, Appl. Comput. Harmon. Anal. 24 (2) (2008) 225-250]. They are based on comparing local quantities rather than on filtering and thresholding. This comparison process is invariant under certain transformations that model light changes in the image, hence we obtain edge detection algorithms which are insensitive to changes in illumination.

Intracrystalline Diffusion of Benzene in Ga-Silicate

1991

Abstract The sorption kinetics of benzene in large Ga-MFI crystals was investigated under constant volume- variable pressure conditions. A complete analysis of the uptake curves has been performed using solution of a nonlinear Volterra equation which describes the interaction of uptake process with the apparatus. Within the time scale of uptake measurements (10 3 -10 4 s) the uptake curves were found to be consistent with the solution of the second Fick's law. Corrected diffusion coefficients were found to be essentially independent of loading within the loading range investigated and in contrast to the system benzene-HNaZSM-5 [1,2] their temperature dependence is much stronger.

Eigenvalue Accumulation for Singular Sturm–Liouville Problems Nonlinear in the Spectral Parameter

1999

Abstract For certain singular Sturm–Liouville equations whose coefficients depend continuously on the spectral parameter λ in an interval Λ it is shown that accumulation/nonaccumulation of eigenvalues at an endpoint ν of Λ is essentially determined by oscillatory properties of the equation at the boundary λ = ν . As applications new results are obtained for the radial Dirac operator and the Klein–Gordon equation. Three other physical applications are also considered.

Non-Lipschitz Homogeneous Volterra Integral Equations

2018

In this chapter we introduce a class of nonlinear Volterra integral equations (VIEs) which have certain properties that deviate from the standard results in the field of integral equations. Such equations arise from various problems in shock wave propagation with nonlinear flux conditions. The basic equation we will consider is the nonlinear homogeneous Hammerstein–Volterra integral equation of convolution type $$\displaystyle u(t) = \int _0^t k(t-s) g(u(s))\,\mathrm {d}s. $$ When g(0) = 0, this equation has function u ≡ 0 as a solution (trivial solution). It is interesting to determine whether there exists a nontrivial solution or not. Classical results on integral equations are not to be …

H<inf>∞</inf> control of markovian switching systems with time-delays: Applied to DC-DC converters

2011

The DC-DC switching power converters are highly nonlinear systems. Consequently, the conventional linear controls based on averaging and linearization techniques will result in poor dynamic performance or system instability. In order to resolve this problem, in this paper a robust state feedback H∞ control is proposed for these systems under Markovian switching with mixed discrete, neutral and distributed delays. Based on the Lyapunov-Krasovskii functional theory, some required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired control is de…

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.