POSITIVE PERIODIC SOLUTIONS OF THE FIRST-ORDER SINGULAR DISCRETE SYSTEMS

In this paper, we study two kinds of first-order singular discrete systems. By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.

Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Delay-dependent robust control for uncertain discrete singular systems with time-varying delay

The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.

Reachability analysis of switched linear discrete singular systems

This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.

Audio Zero-Watermark Scheme Based on Discrete Cosine Transform-Discrete Wavelet TransformSingular Value Decomposition

Traditional watermark embedding schemes inevitably modify the data in a host audio signal and lead to the degradation of the host signal.In this paper,a novel audio zero-watermarking algorithm based on discrete wavelet transform(DWT),discrete cosine transform(DCT),and singular value decomposition(SVD) is presented.The watermark is registered by performing SVD on the coefficients generated through DWT and DCT to avoid data modification and host signal degradation.Simulation results show that the proposed zero-watermarking algorithm is strongly robust to common signal processing methods such as requantization,MP3 compression,resampling,addition of white Gaussian noise,and low-pass filtering.

DISCRETE SINGULAR CONVOLUTION METHOD WITH PERFECTLY MATCHED ABSORBING LAYERS FOR THE WAVE SCATTERING BY PERIODIC STRUCTURES

A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.

A New Method of State Estimation for Singular Discrete-time Stochastic Linear System

Using theory of Bayesian Dynamic Models and Forecasting , this paper mainly deals with the problem on state estimation for singular discrete time stochastic linear system. And a new method of state estimation linear Bayes estimation (LBE for short) has been proposed.

EFFICIENT NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FLEXIBLE ROD HIT BY RIGID BALL

Impact dynamics of flexible solids is important in engineering practice. Obtaining its dynamic response is a challenging task and usually achieved by numerical methods. The objectives of the study are twofold. Firstly, the discrete singular convolution （DSC） is used for the first time to analyze the impact dynamics. Secondly, the efficiency of various numerical methods for dynamic analysis is explored via an example of a flexible rod hit by a rigid ball. Three numerical methods, including the conventional finite element （FE） method, the DSC algorithm, and the spectral finite element （SFE） method, and one proposed modeling strategy, the improved spectral finite element （ISFE） method, are involved. Numerical results are compared with the known analytical solutions to show their efficiency. It is demonstrated that the proposed ISFE modeling strategy with a proper length of con- ventional FE yields the most accurate contact stress among the four investigated models. It is also found that the DSC algorithm is an alternative method for collision problems.

DISCRETE APPROXIMATIONS FOR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH PARABOLIC LAYERS,Ⅱ

In his series of three papers we study singularly perturbed (SP) boundary valueproblems for equations of elliptic and parabolic type. For small values of the pertur-bation parameter parabolic boundary and interior layers appear in these problems.If classical discretisation methods are used, the solution of the finite differencescheme and the approximation of the diffusive flux do not converge uniformly withrespect to this parameter. Using the method of special, adapted grids, we canconstruct difference schemes that allow approximation of the solution and the nor-malised diffusive flux uniformly with respect to the small parameter.We also consider sillgularly perturbed boundary value problems for convection-diffusion equations. Also for these problems we construct special finite differenceschemes, the solution of which converges ε-uniformly We study what problems ap-pear, when classical schemes are used for the approximation of the spatial deriva-tives. We compare the results with those obtained by the adapted approach. Re-sults of numerical experiments are discussed.In the three papers we first give an introduction on the general problem, andthen we consider respectively (i) Problems for SP parabolic equations, for whichthe solution and the normalised diffusive fluxes are required; (ii) Problems for SPelliptic equations with boundary conditions of Diriclilet, Neumann and RDbin type;(iii) Problems for SP parabolic equation with discontinuous boundary conditions-

Nonlinear Analysis of Organic Polymer Solar Cells Using Differential Quadrature Technique with Distinct and Unique Shape Function

Four numerical schemes are introduced for the analysis of photocurrent transients in organic photovoltaic devices.Themathematicalmodel for organic polymer solar cells contains a nonlinear diffusion-reaction partial differential equation system with electrostatic convection attached to a kinetic ordinary differential equation.To solve the problem,Polynomial-based differential quadrature,Sinc,and Discrete singular convolution are combined with block marching techniques.These schemes are employed to reduce the problem to a nonlinear algebraic system.The iterative quadrature technique is used to solve the reduced problem.The obtained results agreed with the previous exact one and the finite element method.Further,the effects of different times,different mobilities,different densities,different geminate pair distances,different geminate recombination rate constants,different generation efficiencies,and supporting conditions on photocurrent have been analyzed.The novelty of this paper is that these schemes for photocurrent transients in organic polymer solar cells have never been presented before,so the results may be useful for improving the performance of solar cells.

DISCRETE APPROXIMATIONS FOR SINGULARLY PERTURBED BOUNDARY VALUE PEOBLEMS WITH PARABOLIC LAYERS,I

In this series of three papers we study singularly perturbed (SP) boundaryvalue problems for equations of eiliptic and parabolic type- For small values ofthe perturbation parameter parabolic boundary and interior layers appear in theseproblems. If classical discretisation methods are used, the solution of the finitedifference scheme and the approximation of the diffusive flux do not converge uniformly with respect to this parameter. Using the method of special, edapted grids,we can construct difference schemes that allow apprcximation of the solution andthe normalised diffusive flux uniformly with respect to the small parameter.We also consider singularly perturbed boundary value problems for convection-diffusion equations. Also for these problems we construct special finite differenceschemes, the solution of which converges ε-uniformly. We study what problems appear, when classical schemes are used for the approximation of the spatial derivatives. We compare the results with those obtained by the adapted approach. Re-sults of numerical experiments are discussed.In the three papers we first give an introduction on the general problem, andthen we consider respectively (i) Problems for SP parabolic equations, for whichthe solution and the normalised diffusive fluxes are required; (ii) Problems for SPelliptic equations with boundary conditions of Dirichlet, Neumann and Robin type;(iii) Problems for SP parabolic equation with discontinuous boundary conditions.

DISCRETE APPROXIMATIONS FOR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH PARABOLIC LAYERS, III

In this series of three papers we study singularly perturbed (SP) boundary vaue problems for equations of elliptic and parabolic troe. For small values of the perturbation parameter parabolic boundary and interior layers appear in these problems. If classical discretisation methods are used, the solution of the finite difference scheme and the approximation of the diffusive flux do not converge uniformly with respect to this parameter. Using the method of special, adapted grids,we can construct difference schemes that allow approkimation of the solution and the normalised diffusive flux uniformly with respect to the small parameter.We also consider singularly perturbed boundary value problems for convection diffusion equations. Also for these problems we construct special finite difference schemes, the solution of which converges E-uniformly We study what problems appear, when classical schemes are used for the approximation of the spatial deriva tives. We compare the results with those obtained by the adapted approach. Results of numerical experiments are discussed.In the three papers we first give an introduction on the general problem, and then we consider respectively (i) Problems for SP parabolic equations, for which the solution and the normalised diffusive fluxes are required; (ii) Problems for SP elliptic equations with boundary conditions of Dirichlet, Neumann and Robin type;(iii) Problems for SP parabolic eqllation with discontinuous boundaxy conditions