Erratum a correction on the stability of implicit higher order difference systems

1995 ◽  
Vol 71 (1) ◽  
pp. 91-96
Author(s):  
L. Jódar ◽  
E. Navarro ◽  
M.V. Ferrer
Keyword(s):  
Higher Order ◽  
Order Difference ◽  
Difference Systems ◽  
The Stability

scholarly journals On the Stability of Linear Incommensurate Fractional-Order Difference Systems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1754
Author(s):  
Noureddine Djenina ◽  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Giuseppe Grassi ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Difference Equations ◽  
Equivalent System ◽  
Stability Of Solutions ◽  
Extended Version ◽  
Transform Method ◽  
Order Difference ◽  
Difference Systems ◽  
The Stability

To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.

scholarly journals Stability Analysis of a Class of Higher Order Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yuanyuan Liu ◽  
Fanwei Meng
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonlinear Difference Equations ◽  
Order Difference ◽  
Finite Dimensional ◽  
Infinite Delays ◽  
Stability And Instability ◽  
The Stability ◽  
The Right

We consider the sufficient conditions for asymptotic stability and instability of certain higher order nonlinear difference equations with infinite delays in finite-dimensional spaces. With the aid of the general comparison condition on the right-hand side functionfk(·), we generalize the stability and instability result.

scholarly journals Novel convenient conditions for the stability of nonlinear incommensurate fractional-order difference systems

2021 ◽  
Author(s):  
Mohd Taib Shatnawi ◽  
Noureddine Djenina ◽  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Giuseppe Grassi
Keyword(s):  
Fractional Order ◽  
Order Difference ◽  
Difference Systems ◽  
The Stability

Stability of fractional variable order difference systems

2019 ◽  
Vol 22 (3) ◽  
pp. 807-824
Author(s):  
Dorota Mozyrska ◽  
Piotr Oziablo ◽  
Małgorzata Wyrwas
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Variable Order ◽  
Order Difference ◽  
Discrete Time Systems ◽  
Difference Systems ◽  
The Stability ◽  
Definition Of ◽  
The Right ◽  
Time Systems

Abstract The problem of stability of the Grünwald-Letnikov-type linear fractional variable order discrete-time systems is discussed. As a definition of the Grünwald-Letnikov difference is a convolution type, the 𝓩-transform is used as an effective tool for the stability analysis. The conditions for asymptotic stability and for instability are presented. In the case of a scalar system we state conditions that guarantee asymptotic stability in inequalities for a coefficient that appears on the right hand side of the equation defined the system}. We describe regions of the stability for systems accordingly to locus of eigenvalues of a matrix associated to the considered system. In the general case of the linear difference systems one can determine the regions of location of eigenvalues of matrices associated to the systems in order to guarantee the asymptotic stability of the considered systems. Some of the frames of these regions are illustrated in the examples.

Stability of Equilibrium Solutions in Planar Hamiltonian Difference Systems

2015 ◽  
Vol 67 (6) ◽  
pp. 1270-1289
Author(s):  
Cristian Carcamo ◽  
Claudio Vidal
Keyword(s):  
Hamiltonian Systems ◽  
Linear Hamiltonian System ◽  
Equilibrium Solutions ◽  
Order Difference ◽  
First Order ◽  
Difference Systems ◽  
Linear Hamiltonian Systems ◽  
The Stability ◽  
Cubic Polynomials ◽  
Lyapunov Sense

AbstractIn this paper, we study the stability in the Lyapunov sense of the equilibrium solutions of discrete or difference Hamiltonian systems in the plane. First, we perform a detailed study of linear Hamiltonian systems as a function of the parameters. In particular we analyze the regular and the degenerate cases. Next, we give a detailed study of the normal form associated with the linear Hamiltonian system. At the same time we obtain the conditions under which we can get stability (in linear approximation) of the equilibrium solution, classifying all the possible phase diagrams as a function of the parameters. After that, we study the stability of the equilibrium solutions of the first order difference system in the plane associated with mechanical Hamiltonian systems and Hamiltonian systems defined by cubic polynomials. Finally, we point out important diòerences with the continuous case.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

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