One of the most frequently used techniques to solve polynomial eigenvalue problems is linearization, in which the polynomial eigenvalue problem is turned into an equivalent linear eigenvalue problem with the same eigenvalues, and with easily recoverable eigenvectors. The eigenvalues and eigenvectors of the linearization are usually computed using a backward stable solver such as the QZ algorith...

This paper discusses the problem of using feedback and coordinates transformation in order to transform a given nonlinear system with outputs into a controllable and observable linear one. We discuss separately the effect of change of coordinates and, successively, the effect of both change of coordinates and feedback transformation. One of the main results of the paper is to show what extra co...

Solar energy can be captured by Photovoltaics (PV) and converted into electrical power. This power then connected to grids electronic converters, which also operate the PV panels at around their maximum point (MPP), maximizing harvested energy. When are in an array, partial shading effect generates a distortion of curve result loss since tracking algorithms might not able detect MPP. To solve t...

This paper is a survey of some results obtained in evolutionary genetics by algebraical methods. The main topics: 1 . Some special classes bf algebras which arising in population genetics (stochastic. haric, RmtxsTEINian, genetic etc.). 2. The BERNSTEIS’S problem and the stationary genetic structure. 3. The convergence to an equilibrium. the rate of convergence. 4. The exact linearization of ev...

In this paper, we study the tracking control problem for a nonlinear system in which the zero dynamics may be unstable. The objective here is to approximate the nonlinear system by another singularly perturbed system by using a small singular perturbation parameter  . The proposed approach is based on the methodology of exact input output linearization control, the integrator backstepping appr...