Frequency-domain dissipativity analysis for output negative imaginary systems allowing imaginary-axis poles

Parijat Bhowmick, Nitisha Bordoloi, Alexander Lanzon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This brief addresses the frequency-domain dissipativity problem of a broader class of Output Negative Imaginary systems, termed as the time-domain ONI (or TDONI) systems, which have been defined in the time domain w.r.t. an abstract energy supply rate function. This definition encompasses the existing strict/non-strict NI subsets, including those having imaginary-axis poles. This paper introduces the idea of a “shifted (Qσ(ω); Sσ(ω);Rσ(ω))-dissipativity”, as an alternative to the conventional (Q(ω); S(ω);R(ω))-dissipativity, to capture the TD-ONI systems, particularly the ones having imaginaryaxis poles. The shifted (Qσ(ω); Sσ(ω);Rσ(ω))-dissipativity is defined w.r.t. a shifted imaginary axis (σ + jω; σ > 0) and thereby, it overcomes the limitation of earlier frequency-domain dissipative frameworks to capture systems with imaginary-axis poles. The paper has also established the relationship between the time-domain and frequency-domain dissipativity of TD-ONI systems. Finally, a closed-loop stability theorem is also given for a positive feedback interconnection of two TD-ONI systems.
Original languageEnglish
Title of host publicationProceedings of the 21st European Control Conference, Bucharest, Romania, Jun 2023
Publication statusAccepted/In press - 20 Mar 2023
Event21st European Control Conference - Bucharest, Romania
Duration: 13 Jun 202316 Jun 2023


Conference21st European Control Conference
Abbreviated titleECC


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