© The Institution of Engineering and Technology
In this study, the problem of finding state bounds is considered, for the first time, for a class of positive timedelay coupled differentialdifference equations (CDDEs) with bounded disturbances. First, the authors present a novel method, which is based on nonnegative matrices and optimisation techniques, for computing a likeexponential componentwise upper bound of the state vector of the CDDEs without disturbances. The main idea is to establish bounds of the state vector on finitetime 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, they 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 the obtained results is illustrated through a numerical example.
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