On Topological Entropy of Interconnected Nonlinear Systems

Daniel Liberzon

doi:10.1109/LCSYS.2021.3069735

On Topological Entropy of Interconnected Nonlinear Systems

Research output: Contribution to journal › Article › peer-review

Abstract

We study topological entropy of a nonlinear system represented as an interconnection of smaller subsystems. Under suitable assumptions on the Jacobian matrices characterizing the interconnection, we obtain an explicit upper bound on the entropy of the overall system, and show that it can be related to upper bounds on the entropies of the subsystems. We also analyze in detail the special case of a cascade connection of two subsystems, establishing an upper bound on the entropy which is more tightly linked to individual entropy bounds for the subsystems.

Original language	English (US)
Article number	9390224
Pages (from-to)	2210-2214
Number of pages	5
Journal	IEEE Control Systems Letters
Volume	5
Issue number	6
DOIs	https://doi.org/10.1109/LCSYS.2021.3069735
State	Published - Dec 2021

Keywords

Information theory and control
quantized systems
stability of nonlinear systems

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization

Online availability

10.1109/LCSYS.2021.3069735License: CC BY

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abstract = "We study topological entropy of a nonlinear system represented as an interconnection of smaller subsystems. Under suitable assumptions on the Jacobian matrices characterizing the interconnection, we obtain an explicit upper bound on the entropy of the overall system, and show that it can be related to upper bounds on the entropies of the subsystems. We also analyze in detail the special case of a cascade connection of two subsystems, establishing an upper bound on the entropy which is more tightly linked to individual entropy bounds for the subsystems. ",

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note = "Funding Information: Manuscript received January 4, 2021; revised March 9, 2021; accepted March 12, 2021. Date of publication March 30, 2021; date of current version April 28, 2021. This work was supported in part by the NSF under Grant CMMI-1662708, and in part by Air Force Office of Scientific Research (AFOSR) under Grant FA9550-17-1-0236. Recommended by Senior Editor C. Prieur. Publisher Copyright: {\textcopyright} 2017 IEEE.",

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N2 - We study topological entropy of a nonlinear system represented as an interconnection of smaller subsystems. Under suitable assumptions on the Jacobian matrices characterizing the interconnection, we obtain an explicit upper bound on the entropy of the overall system, and show that it can be related to upper bounds on the entropies of the subsystems. We also analyze in detail the special case of a cascade connection of two subsystems, establishing an upper bound on the entropy which is more tightly linked to individual entropy bounds for the subsystems.

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KW - quantized systems

KW - stability of nonlinear systems

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On Topological Entropy of Interconnected Nonlinear Systems

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