This paper considers the robust asymptotic closed-loop hyperstability of a nominal time-invariant plant with an associate strongly positive real transfer function subject to unstructured disturbances in the sate and output. Such disturbances are characterized by upper-bounding growing laws of the state and control. It is assumed that the controller is any member within a class which satisfies a Popov´s type integral inequality. The continuous-time nonlinear and perhaps time-varying feedback

more »

... rollers belong to a certain class which satisfies a discrete-type Popov´s inequality. The robust closed-loop hyperstability property is proved under certain explicit conditions of smallness of the coefficients of the upper-bounding functions of the norms of the unstructured disturbances related to the absolute stability abscissa of the modelled part of the nominal feed-forward transfer function. Note that Theorem 9 (i) still holds, that is, the (K, L, M) dissipativity and strict dissipativity of Definitions 5 and 6 hold if Q ≻ 0 and, respectively, Q ≻ 0 irrespective of the system being nominal or not since the properties depend only of the measured input and output. If the system is subject to disturbances, then the following robustness-type extended result from Theorem 9 holds inspired by previous results in Theorem 3: