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

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.

Inspec keywords: time-varying systems; delays; matrix algebra; continuous time systems; difference equations; asymptotic stability; discrete systems; Lyapunov methods

Other keywords: state bounds; positive time-delay; infinite time horizon; differential-difference equations; optimisation techniques; ultimate bounds; state vector; state transformations; componentwise upper bounds; bounded disturbances; CDDEs; finite-time intervals

Subjects: Stability in control theory; Discrete control systems

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