Admissible sets for polytopic linear systems subject to slowly-varying unobservable disturbances

Preprint, 2020

This note describes a method to calculate sets of safe initial conditions for polytopic linear systems subject to slowly-varying unobservable disturbances. Such sets are herein called admissible sets; invariant sets are admissible but admissible sets are not necessarily invariant. By examining conditions for admissible sets of this particular system class, we prove that admissible sets can be calculated by only considering a special property that we call \emph{the $\lambda$-proximal-contraction property} at the vertices of the set that bounds the slowly-varying disturbances. An academic example is used to illustrate how to apply the method, and a discussion follows that summarizes the main points.