Necessary and Sufficient Conditions for Assignability of the Lyapunov Spectrum of Discrete Linear Time-Varying Systems

Artur Babiarz; Irina Banshchikova; Adam Czornik; Evgenii K. Makarov; Michal Niezabitowski; Svetlana Popova

doi:10.1109/TAC.2018.2823086

Necessary and Sufficient Conditions for Assignability of the Lyapunov Spectrum of Discrete Linear Time-Varying Systems

Artur Babiarz
, Irina Banshchikova
, Adam Czornik
, Evgenii K. Makarov
, Michal Niezabitowski
, Svetlana Popova

Department of Automatic Control and Robotics (RAU/RAU3)

Udmurt State University
Belarus Academy of Sciences
Ural Branch of the Russian Academy of Sciences

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

27 Citations (Scopus)

Abstract

We consider a version of the pole assignment problem for linear discrete time-varying systems with linear state feedback. Our aim is to prove that all the systems from the closure (in the topology of pointwise convergence) of all shifts of the original system have an assignable Lyapunov spectrum if and only if the original system is uniformly completely controllable. We also provide an example to show that uniform complete controllability is not a necessary condition for assignability of the Lyapunov spectrum of the original system.

Original language	English
Article number	8331115
Pages (from-to)	3825-3837
Number of pages	13
Journal	IEEE Transactions on Automatic Control
Volume	63
Issue number	11
DOIs	https://doi.org/10.1109/TAC.2018.2823086
Publication status	Published - Nov 2018

Keywords

Discrete time-varying systems
Lyapunov spectrum
pole assignment problem
uniform complete controllability

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2018.2823086

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title = "Necessary and Sufficient Conditions for Assignability of the Lyapunov Spectrum of Discrete Linear Time-Varying Systems",

abstract = "We consider a version of the pole assignment problem for linear discrete time-varying systems with linear state feedback. Our aim is to prove that all the systems from the closure (in the topology of pointwise convergence) of all shifts of the original system have an assignable Lyapunov spectrum if and only if the original system is uniformly completely controllable. We also provide an example to show that uniform complete controllability is not a necessary condition for assignability of the Lyapunov spectrum of the original system.",

keywords = "Discrete time-varying systems, Lyapunov spectrum, pole assignment problem, uniform complete controllability",

author = "Artur Babiarz and Irina Banshchikova and Adam Czornik and Makarov, \{Evgenii K.\} and Michal Niezabitowski and Svetlana Popova",

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year = "2018",

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AU - Babiarz, Artur

AU - Banshchikova, Irina

AU - Czornik, Adam

AU - Makarov, Evgenii K.

AU - Niezabitowski, Michal

AU - Popova, Svetlana

PY - 2018/11

Y1 - 2018/11

N2 - We consider a version of the pole assignment problem for linear discrete time-varying systems with linear state feedback. Our aim is to prove that all the systems from the closure (in the topology of pointwise convergence) of all shifts of the original system have an assignable Lyapunov spectrum if and only if the original system is uniformly completely controllable. We also provide an example to show that uniform complete controllability is not a necessary condition for assignability of the Lyapunov spectrum of the original system.

AB - We consider a version of the pole assignment problem for linear discrete time-varying systems with linear state feedback. Our aim is to prove that all the systems from the closure (in the topology of pointwise convergence) of all shifts of the original system have an assignable Lyapunov spectrum if and only if the original system is uniformly completely controllable. We also provide an example to show that uniform complete controllability is not a necessary condition for assignability of the Lyapunov spectrum of the original system.

KW - Discrete time-varying systems

KW - Lyapunov spectrum

KW - pole assignment problem

KW - uniform complete controllability

UR - https://www.scopus.com/pages/publications/85055971845

U2 - 10.1109/TAC.2018.2823086

DO - 10.1109/TAC.2018.2823086

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 11

M1 - 8331115

ER -

Necessary and Sufficient Conditions for Assignability of the Lyapunov Spectrum of Discrete Linear Time-Varying Systems

Abstract

Keywords

ASJC Scopus subject areas

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