Uniform Detectability of Linear Time Varying Systems With Exponential Dichotomy

Markus Tranninger; Richard Seeber; Martin Steinberger; Martin Horn

doi:10.1109/LCSYS.2020.2992818

Uniform Detectability of Linear Time Varying Systems With Exponential Dichotomy

Markus Tranninger^*, Richard Seeber, Martin Steinberger, Martin Horn

^*Corresponding author for this work

Institute of Automation and Control (4430)

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

Abstract

Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow, uniformly and exponentially. This letter studies uniform detectability and observability notions for linear time varying systems, which admit an exponential dichotomy. The main contributions are necessary and sufficient detectability conditions for this class of systems.

Original language	English
Article number	9088145
Pages (from-to)	809-814
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	4
Issue number	4
Early online date	6 May 2020
DOIs	https://doi.org/10.1109/LCSYS.2020.2992818
Publication status	Published - Oct 2020

Keywords

observers for linear systems
stability of linear systems
Time varying systems

ASJC Scopus subject areas

Control and Optimization
Control and Systems Engineering

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1109/LCSYS.2020.2992818

https://arxiv.org/abs/2004.10533

Cite this

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title = "Uniform Detectability of Linear Time Varying Systems With Exponential Dichotomy",

abstract = "Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow, uniformly and exponentially. This letter studies uniform detectability and observability notions for linear time varying systems, which admit an exponential dichotomy. The main contributions are necessary and sufficient detectability conditions for this class of systems.",

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AU - Horn, Martin

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AB - Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow, uniformly and exponentially. This letter studies uniform detectability and observability notions for linear time varying systems, which admit an exponential dichotomy. The main contributions are necessary and sufficient detectability conditions for this class of systems.

KW - observers for linear systems

KW - stability of linear systems

KW - Time varying systems

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Uniform Detectability of Linear Time Varying Systems With Exponential Dichotomy

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

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