This book is supposed to serve as an introduction to the theory of invariance entropy which
is related to the control task of making a subset in the state space of a control system …

For discrete-time control systems, notions of entropy for invariance are compared. One is
based on feedbacks, and the other one on open-loop control functions. Under a strong …

The paper deals with observation of nonlinear and deterministic, though maybe chaotic,
discrete-time systems via finite capacity communication channels. We introduce several …

Minimal bit rates and entropy are studied for exponential stabilization of control systems in
continuous time. Upper and lower bounds for the stabilization entropy are derived. In …

The paper deals with the state estimation problem for nonlinear dynamical systems via
communication channels with limited data rate. We introduce several minimum data-rate …

This paper is concerned with the rate at which a discrete-time, deterministic, and possibly
large network of nonlinear systems generates information, and so with the minimum rate of …

Topological feedback entropy (TFE) measures the intrinsic rate at which a continuous, fully
observed, deterministic control system generates information for controlled set-invariance. In …

This paper is concerned with the following problem: Given a stochastic nonlinear system
controlled over a noisy channel, what is the largest class of channels for which there exist …

For linear (control) systems on infinite-dimensional state spaces with finite-dimensional
unstable subspace, this paper introduces the concepts of topological entropy and invariance …

The paper deals with observation of nonlinear and deterministic, though maybe chaotic,
discrete-time systems via finite capacity communication channels. We consider various …