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Comparison between Different Notions of Stability for Laurent Systems

Athalye, CD and Pal, D and Pillai, HK (2021) Comparison between Different Notions of Stability for Laurent Systems. In: IEEE Transactions on Automatic Control, 66 (2). pp. 768-772.

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Official URL: https://dx.doi.org/10.1109/TAC.2020.2976297


In this article, we examine a particular family of infinite-dimensional discrete autonomous systems given by a firstorder state-space equation; the state transition matrix for this family is a Laurent polynomial matrix A(,-1), where is the shift operator on Rn-valued sequences. We term this family of systems as Laurent systems. We give necessary and sufficient conditions for the exponential 2-stability and the exponential-stability of Laurent systems. We also compare the following four different notions of stability for Laurent systems: The 2-stability, the exponential 2-stability, the-stability, and the exponential-stability; furthermore, we conclude that the 2-stability is an outlier. © 1963-2012 IEEE.

Item Type: Journal Article
Publication: IEEE Transactions on Automatic Control
Publisher: Institute of Electrical and Electronics Engineers Inc.
Additional Information: The copyright of this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords: Equations of state, Autonomous systems; First-order; Infinite dimensional; Laurent polynomial; Shift operators; State space equation; State transition Matrix, System stability
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 26 Feb 2021 06:00
Last Modified: 26 Feb 2021 06:00
URI: http://eprints.iisc.ac.in/id/eprint/68004

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