On asymptotically periodic linear systems

Delay-Dependent Robust Asymptotically Stable for Linear Time Variant Systems

In this paper, the problem of delay dependent robust asymptotically stable for uncertain linear time-variant system with multiple delays is investigated. A new delay-dependent stability sufficient condition is given by using the Lyapunov method, linear matrix inequality (LMI), parameterized first-order model transformation technique and transformation of the interval uncertainty in to the norm ...

On Asymptotically Periodic Solutions of Linear Discrete Volterra Equations

We show that a class of linear nonconvolution discrete Volterra equations has asymptotically periodic solutions. We also examine an example for which the calculations can be done explicitly. The results are established using theorems on the boundedness and convergence to a finite limit of solutions of linear discrete Volterra equations.

Existence of Periodic Solutions for a Class of Asymptotically p-Linear Discrete Systems Involving p-Laplacian

Periodic Linear Systems

when A is a continuous periodic n× n matrix function of t; i.e., when there is a constant T > 0 such that A(t + T ) = A(t) for every t ∈ R. When that condition is satisfied, we say, more precisely, that A is T -periodic. If T is the smallest positive number for which this condition holds, we say that T is the minimal period of A. Let A be T -periodic, and let X(t) be a fundamental matrix for (1...

Poincaré-birkhoff Fixed Point Theorem and Periodic Solutions of Asymptotically Linear Planar Hamiltonian Systems

This work, which has a self contained expository character, is devoted to the Poincaré-Birkhoff (PB) theorem and to its applications to the search of periodic solutions of nonautonomous periodic planar Hamiltonian systems. After some historical remarks, we recall the classical proof of the PB theorem as exposed by Brown and Neumann. Then, a variant of the PB theorem is considered, which enables...