1 research outputs found
State bounding for positive coupled differential - difference equations with bounded disturbances
In this paper, the problem of finding state bounds is considered, for the
first time, for a class of positive time-delay coupled differential-difference
equations (CDDEs) with bounded disturbances. First, we present a novel method,
which is based on nonnegative matrices and optimization techniques, for
computing a like-exponential componentwise upper bound of the state vector of
the CDDEs without disturbances. The main idea is to establish bounds of the
state vector on finite-time intervals and then, by using the solution
comparison method and the linearity of the system, extend to infinite time
horizon. Next, by using state transformations, we extend the obtained results
to a class of CDDEs with bounded disturbances. As a result, componentwise upper
bounds, ultimate bounds and invariant set of the perturbed system are obtained.
The feasibility of obtained results are illustrated through a numerical
example.Comment: 24 pages, 5 figure