Some modifications of the Weiss–Staffans perturbation theorem

Summary For boundary control systems in factor form, a version of the Weiss perturbation result is derived and formulated as an exponential stability robustness result (Theorem [Theorem 3.1. 3.1 Theorem Let A generate an EXSC0‐semigroup {S(t)}t≥0 on ...]). An example of a heating rod control, illustrating its application, is given. Next, a generalization of the Weiss perturbation to a class of retarded systems of the neutral type is presented (Theorem [Theorem 4.1. 4.1 Theorem The closed‐loop system operator generates an EXSC0‐semigroup, ...]). The characteristic feature of this generalization is that it allows to deal with a dynamic perturbation rather than a static one. Using this result, we get a new derivation of an exponential stability criterion. We also show that some parabolic systems without the admissibility of control operator still admit a weakened version of the Weiss perturbation result (Theorem [Theorem 5.1. 5.1 Theorem Let A generate an EXS analytic semigroup ...]). This result is a consequence of the necessary and sufficient conditions for generation of an analytic exponentially stable semigroup and some frequency‐domain estimates and is illustrated in details by an example of an unloaded electric R C ‐transmission line. Copyright © 2016 John Wiley & Sons, Ltd.