We study the global result, boundedness, and periodicity of solutions of the difference equation xn+1 = a+ bxn−l + cxn−k dxn−l + exn−k , n = 0, 1, . . . , where the parameters a, b, c, d, and e are positive real numbers and the initial conditions x−t, x−t+1, . . . , x−1 and x0 are positive real numbers where t = max{l, k}, l 6= k. c ©2016 All rights reserved.

It is well-known that the second-order cone can be outer-approximated to an arbitrary accuracy $\epsilon$ by a polyhedral of compact size defined irrational data. In this paper, we propose two rational outer-approximations retaining same guaranteed $\epsilon$. The first outer-approximation has as optimal but from literature. case,we provide practical approach obtain such approximation smallest ...

In this survey paper we review the methods for stability investigation of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative examples are presented as well. Mathematics Subject Classification: 26A33 (main), 93D25, 30F99

An algorithm to compute a reduced-order model of a linear dynamic system is described. It is based on the rational Krylov method, which is an extension of the shift-and-invert Arnoldi method where several shifts (interpolation points) are used to compute an orthonormal basis for a sub-space. It is discussed how to generate a reduced-order model of a linear dynamic system, in such a way that the...

The equivalent system for a multiple-rational-order (MRO) fractional differential system is studied, where the fractional derivative is in the sense of Caputo or Riemann-Liouville. With the relationship between the Caputo derivative and the generalized fractional derivative, we can change the MRO fractional differential system with a Caputo derivative into a higher-dimensional system with the s...