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State bounding for positive coupled differential-difference equations with bounded disturbances

State bounding for positive coupled differential-difference equations with bounded disturbances

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In this study, 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, the authors present a novel method, which is based on non-negative matrices and optimisation 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, 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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