Componentwise ultimate bounds for positive discrete time-delay systems perturbed by interval disturbances
Nam, Phan T., Trinh, Hieu M. and Pathirana, Pubudu N. 2016, Componentwise ultimate bounds for positive discrete time-delay systems perturbed by interval disturbances, Automatica, vol. 72, pp. 153-157, doi: 10.1016/j.automatica.2016.06.007.
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Componentwise ultimate bounds for positive discrete time-delay systems perturbed by interval disturbances
This paper presents a method to derive componentwise ultimate upper bounds and componentwise ultimate lower bounds for linear positive systems with time-varying delays and bounded disturbances. The disturbance vector is assumed to vary within a known interval whose lower bound may be different from zero. We first derive a sufficient condition for the existence of componentwise ultimate bounds. This condition is given in terms of the spectral radius of the system matrices which is easy to check and allows us to compute directly both the smallest componentwise ultimate upper bound and the largest componentwise ultimate lower bound. Then, by using the comparison method, we extend the obtained result to a class of nonlinear time-delay systems which has linear positive bounds. Two numerical examples are given to illustrate the effectiveness of the obtained results.
010203 Calculus of Variations, Systems Theory and Control Theory 010204 Dynamical Systems in Applications 090602 Control Systems, Robotics and Automation
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