Topological equivalence and structural stability for linear difference equations

Reducibility and Stability Results for Linear System of Difference Equations

Structural Stability and Equivalence of Linear 2D Discrete Systems

We study stability issues for linear two-dimensional (2D) discrete systems by means of the constructive algebraic analysis approach to linear systems theory. We provide a general definition of structural stability for linear 2D discrete systems which coincides with the existing definitions in the particular cases of the classical Roesser and Fornasini-Marchesini models. We then study the preser...

Uniform Asymptotic Stability and Robust Stability for Positive Linear Volterra Difference Equations in Banach Lattices

A dynamical system is called positive if any solution of the system starting from nonnegative states maintains nonnegative states forever. In many applications where variables represent nonnegative quantities we often encounter positive dynamical systems as mathematical models see 1, 2 , and many researches for positive systems have been done actively; for recent developments see, for example, ...

Stability of Stochastic Linear Difference Equations with Varying Delay

Many processes in automatic regulation, physics, mechanics, biology, economy, ecology etc. can be modelled by hereditary systems (see, e.g. [1-3]). One of the main problems for the theory of such systems and their applications is connected with stability [1,2]. Many stability results were obtained by the construction of appropriate Lyapunov functionals. In [4-8] the method is proposed allowing,...

Linear Difference Equations

Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a sys...