Relations between Exponential Dichotomy of Continuous Time-Varying Linear Systems and Bohl Exponents

Adam Czornik

doi:10.1109/TAC.2025.3646014

Relations between Exponential Dichotomy of Continuous Time-Varying Linear Systems and Bohl Exponents

Adam Czornik

Department of Automatic Control and Robotics (RAU/RAU3)

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

Abstract

In this note, we present a new necessary and sufficient condition for having a dichotomy by a continuous linear system with time-varying coefficients. This condition is expressed by Bohl exponents. Based on this condition, we give a formula expressing the spectrum of exponential dichotomy in terms of Bohl exponents. The obtained results are illustrated with a numerical example.

Original language	English
Pages (from-to)	4051-4056
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	71
Issue number	6
DOIs	https://doi.org/10.1109/TAC.2025.3646014
Publication status	Published - 1 Jun 2026

Keywords

Bohl exponents
dichotomy
linear time-varying systems

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2025.3646014

Cite this

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title = "Relations between Exponential Dichotomy of Continuous Time-Varying Linear Systems and Bohl Exponents",

abstract = "In this note, we present a new necessary and sufficient condition for having a dichotomy by a continuous linear system with time-varying coefficients. This condition is expressed by Bohl exponents. Based on this condition, we give a formula expressing the spectrum of exponential dichotomy in terms of Bohl exponents. The obtained results are illustrated with a numerical example.",

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KW - linear time-varying systems

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Relations between Exponential Dichotomy of Continuous Time-Varying Linear Systems and Bohl Exponents

Abstract

Keywords

ASJC Scopus subject areas

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