Assignability of dichotomy spectra for discrete time-varying linear control systems

Le Viet Cuong; Thai Son Doan

doi:10.3934/dcdsb.2020074

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2020, Volume 25, Issue 9: 3597-3607. Doi: 10.3934/dcdsb.2020074

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Assignability of dichotomy spectra for discrete time-varying linear control systems

Le Viet Cuong^1, and
Thai Son Doan^2,3,

1.
Department of Information Technology, National University of Civil Engineering, 55 Giai Phong str., Hanoi, Vietnam
2.
Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam
3.
Thang Long Institute of Mathematics and Applied Sciences, Thang Long University, Nghiem Xuan Yem Road, Hoang Mai, Hanoi, Vietnam

Received: July 31, 2019

Revised: October 31, 2019

Early access: April 2020

Published: September 2020

This research is funded by Vietnam National University of Civil Engineering (NUCE) under grant number 202-2018/KHXD-TD

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Abstract

In this paper, we show that for discrete time-varying linear control systems uniform complete controllability implies arbitrary assignability of dichotomy spectrum of closed-loop systems. This result significantly strengthens the result in [5] about arbitrary assignability of Lyapunov spectrum of discrete time-varying linear control systems.

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Mathematics Subject Classification: Primary: 34A30, 34D09, 34D08, 34H05.

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References

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