The brief review of new methods of factorization, autonomization and exact linearization of the ordinary differential equations is represented. These methods along with the method of the group analysis based on using both point and nonpoint, local and nonlocal transformations are effective tools for study of nonlinear autonomous and nonautonomous dynamical systems. Thus a scope of exactly solva...

Reverse to linearization, we propose a nonlinearization scheme of linear systems for generating integrable equations, based on a simple scaling dimensional argument. This yields together with well known integrable systems, new hierarchies of integrable equations with source terms, allowing exact n-soliton solutions. The novelty of such sources is that they can be deformed recursively by going t...

Abstract-This paper presents a nonlinear control algorithm for a single-stage three-phase buck-boost inverter. In contrast to the linear control law that is formulated according to small signal model that is linearized around an operating point, the exact linearization that is directly based on the large signal model allows for the formulation of the control law over a wide operating range. Mor...

In This Research paper, described different linearization methods in terms of analytical and numerical simulation (Computer added linearized -FE) method Digital image correlation for prediction loading analysis. Article can be helping nonlinearity systems, that what is using likes Numerical (approximation), Analytical (Exact) Experimental. Where, difficult to calculate computers so it uses meth...

A new algorithm is proposed for computing locally the linearizing output of single-input and multi-input nonlinear affine system. The algorithm modifies the extended Goursat normal form to iteratively obtain the successive integrations of one dimensional distributions of control system. The algorithm takes ideas from both vector field approach of feedback linearization and exterior differential...

This paper aims at development of non linear dynamic model for Magnetic Levitation System and proposed linear and nonlinear state space controllers. The linear controller was designed by linearizing the model around equilibrium point, while nonlinear controller was based on feedback linearization where a nonlinear state-space transformation is used to linearize the system exactly. Relative degr...

We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and perfor...

In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization...

This paper presents a novel form of feedback linearization control (FBL) boost-type DC/DC converter: to reach highly accurate output voltage control. Integral action has been inserted into the block diagram scheme. The state-space model boost converter is nonlinear. Accordingly, design procedure controller more complex. modeling and details nonlinear FBL step by step. main goal this highlight i...

Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various ...