Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4628991 | Applied Mathematics and Computation | 2013 | 11 Pages |
Abstract
The asymptotic properties of a real two-dimensional differential system  xâ²(t)=A(t)x(t)+âk=1mBk(t)x(θk(t))+h(t,x(t),x(θ1(t)),â¦,x(θm(t))) with unbounded nonconstant delays t-θk(t)⩾0 satisfying limtââθk(t)=â are studied. Here A,Bk and h are supposed to be matrix functions and a vector function. The conditions for the stability and asymptotic stability of solutions and the conditions under which all solutions tend to zero are given. The methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of a Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Josef Rebenda, ZdenÄk Å marda,