Discrete-time Negative Imaginary Systems from ZOH Sampling

Kanghong Shi; Ian R. Petersen; Igor G. Vladimirov

doi:10.1016/j.ifacol.2024.10.168

Discrete-time Negative Imaginary Systems from ZOH Sampling

Kanghong Shi^*, Ian R. Petersen^*, Igor G. Vladimirov^*

^*Corresponding author for this work

School of Engineering

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

Abstract

A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case.

Original language	English
Pages (from-to)	214-219
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	58
Issue number	17
DOIs	https://doi.org/10.1016/j.ifacol.2024.10.168
Publication status	Published - 1 Aug 2024
Event	26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024 - Cambridge, United Kingdom Duration: 19 Aug 2024 → 23 Aug 2024

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10.1016/j.ifacol.2024.10.168

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title = "Discrete-time Negative Imaginary Systems from ZOH Sampling",

abstract = "A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case.",

keywords = "discrete-time negative imaginary systems, dissipativity, feedback control, stability, zero-order hold sampling",

author = "Kanghong Shi and Petersen, {Ian R.} and Vladimirov, {Igor G.}",

note = "Publisher Copyright: Copyright {\textcopyright} 2024 The Authors.; 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024 ; Conference date: 19-08-2024 Through 23-08-2024",

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doi = "10.1016/j.ifacol.2024.10.168",

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TY - JOUR

T1 - Discrete-time Negative Imaginary Systems from ZOH Sampling

AU - Shi, Kanghong

AU - Petersen, Ian R.

AU - Vladimirov, Igor G.

PY - 2024/8/1

Y1 - 2024/8/1

N2 - A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case.

AB - A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case.

KW - discrete-time negative imaginary systems

KW - dissipativity

KW - feedback control

KW - stability

KW - zero-order hold sampling

UR - http://www.scopus.com/inward/record.url?scp=85210317641&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2024.10.168

DO - 10.1016/j.ifacol.2024.10.168

M3 - Conference article

AN - SCOPUS:85210317641

SN - 2405-8971

VL - 58

SP - 214

EP - 219

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 17

T2 - 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024

Y2 - 19 August 2024 through 23 August 2024

ER -

Discrete-time Negative Imaginary Systems from ZOH Sampling

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