1 / 2017-10-18 15:26:08

Guaranteeing the positivity realness of linear systems with point delays

dynamic systems, positive realness, internal delays, commensurate delays, incommensurate delays

The strict positive realness of transfer functions is a very crucial property to guarantee the global closed-loop asymptotic stability of such feed-forward systems under wide classes of nonlinear eventually time- varying controllers satisfying a certain Popov´s type inequality. The stability is guaranteed for any feedback controller belonging to one such a class. Such a strong asymptotic stability property is known as the asymptotic hyperstability property. The paper investigates the strong / strict positive realness property of systems subject to internal point commensurate and incommensurate constant delays provided that the transfer function of their delay- free counterparts are strong/strict positive real.