Invariance Entropy for Deterministic Control Systems

An Introduction

  • Christoph Kawan

Part of the Lecture Notes in Mathematics book series (LNM, volume 2089)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Christoph Kawan
    Pages 1-42
  3. Christoph Kawan
    Pages 43-87
  4. Christoph Kawan
    Pages 89-105
  5. Christoph Kawan
    Pages 107-120
  6. Christoph Kawan
    Pages 151-175
  7. Christoph Kawan
    Pages 177-220
  8. Back Matter
    Pages 221-272

About this book


This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.


Controlled Invariance Feedback Entropy Invariance Entropy Minimal Data Rates

Authors and affiliations

  • Christoph Kawan
    • 1
  1. 1.Institute of MathematicsUniversity of AugsburgAugsburgGermany

Bibliographic information