Componentwise state bounding of positive time-delay systems with disturbances bounded by a time-varying function

This paper proposes a new method to solve the problem of finding the smallest componentwise upper bound of the state vector of a class of positive time-delay systems perturbed by unknown-but-bounded disturbances. Different from existing methods, which use only the constant maximum bound of the disturbance vector, our method exploits its known time-varying upper bound. As a result, a smaller upper bound, i.e. a more accurate state bound, is derived. A numerical example with some simulations is given to illustrate the effectiveness of our proposed method.