Asymptotic hyperstability under unstructured and structured modeling deviations from the linear behavior

This paper deals with the asymptotic hyperstability of nominally asymptotic hyperstable linear systems in the presence of unstructured modeling errors. It is assumed that the nominal plant is linear, time-invariant and of strictly positive real transfer function with the feedback loop satisfying a Popov's type input–output time integral inequality for all time and the combination resulting in an asymptotically hyperstable closed-loop system. The current plant is assumed to be subjected, in general, unstructured deviations from its nominal behavior but then asymptotic hyperstability results are also obtained for particular structured modeling errors like time-varying linear dynamics, bilinear or delay-dependent dynamics. The key technique used for obtaining the results is to guarantee that a measure of the input/output energy of the forward current dynamics is positive and uniformly bounded for all time for certain amounts of modeling errors provided that the nominal one exhibits the same property.