Abstract: In this study, we have investigated the strict stability
of fuzzy differential systems and we compare the classical notion of
strict stability criteria of ordinary differential equations and the notion
of strict stability of fuzzy differential systems. In addition that, we
present definitions of stability and strict stability of fuzzy differential
equations and also we have some theorems and comparison results.
Strict Stability is a different stability definition and this stability
type can give us an information about the rate of decay of the
solutions. Lyapunov’s second method is a standard technique used
in the study of the qualitative behavior of fuzzy differential systems
along with a comparison result that allows the prediction of behavior
of a fuzzy differential system when the behavior of the null solution
of a fuzzy comparison system is known. This method is a usefull
for investigating strict stability of fuzzy systems. First of all, we
present definitions and necessary background material. Secondly, we
discuss and compare the differences between the classical notion
of stability and the recent notion of strict stability. And then, we
have a comparison result in which the stability properties of the null
solution of the comparison system imply the corresponding stability
properties of the fuzzy differential system. Consequently, we give
the strict stability results and a comparison theorem. We have used
Lyapunov second method and we have proved a comparison result
with scalar differential equations.
Abstract: In this paper, the problem of stability and stabilization
for neutral delay-differential systems with infinite delay is
investigated. Using Lyapunov method, new delay-independent
sufficient condition for the stability of neutral systems with infinite
delay is obtained in terms of linear matrix inequality (LMI).
Memory-less state feedback controllers are then designed for the
stabilization of the system using the feasible solution of the resulting
LMI, which are easily solved using any optimization algorithms.
Numerical examples are given to illustrate the results of the proposed
methods.
Abstract: In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential
(VID) equation is considered. The method is developed by means
of the Legendre wavelet approximation and collocation method. The
properties of Legendre wavelet together with Gaussian integration
method are utilized to reduce the problem to the solution of nonlinear
programming one. Some numerical examples are given to confirm the
accuracy and ease of implementation of the method.
Abstract: This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.
Abstract: In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.
Abstract: In this paper, the criteria of Ψ-eventual stability have been established for generalized impulsive differential systems of multiple dependent variables. The sufficient conditions have been obtained using piecewise continuous Lyapunov function. An example is given to support our theoretical result.
Abstract: In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.
Abstract: Modeling transfer phenomena in several chemical
engineering operations leads to the resolution of partial differential
equations systems. According to the complexity of the operations
mechanisms, the equations present a nonlinear form and analytical
solution became difficult, we have then to use numerical methods
which are based on approximations in order to transform a
differential system to an algebraic one.Finite element method is one
of numerical methods which can be used to obtain an accurate
solution in many complex cases of chemical engineering.The packed
columns find a large application like contactor for liquid-liquid
systems such solvent extraction. In the literature, the modeling of this
type of equipment received less attention in comparison with the
plate columns.A mathematical bidimensionnal model with radial and
axial dispersion, simulating packed tower extraction behavior was
developed and a partial differential equation was solved using the
finite element method by adopting the Galerkine model. We
developed a Mathcad program, which can be used for a similar
equations and concentration profiles are obtained along the column.
The influence of radial dispersion was prooved and it can-t be
neglected, the results were compared with experimental concentration
at the top of the column in the extraction system:
acetone/toluene/water.