Feedback stability analysis via dissipativity with dynamic supply rates

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-12-02 DOI:10.1016/j.automatica.2024.112000

Sei Zhen Khong , Chao Chen , Alexander Lanzon

{"title":"Feedback stability analysis via dissipativity with dynamic supply rates","authors":"Sei Zhen Khong , Chao Chen , Alexander Lanzon","doi":"10.1016/j.automatica.2024.112000","DOIUrl":null,"url":null,"abstract":"<div><div>We propose a general notion of dissipativity with dynamic supply rates for nonlinear systems. This extends classical dissipativity with static supply rates and dynamic supply rates of miscellaneous quadratic forms. The main results of this paper concern Lyapunov and asymptotic stability analysis for nonlinear feedback dissipative systems that are characterised by dissipation inequalities with respect to compatible dynamic supply rates but involving possibly different and independent auxiliary systems. Importantly, dissipativity conditions guaranteeing stability of the state of the feedback systems, without concerns on the stability of the state of the auxiliary systems, are provided. The key results also specialise to a simple coupling test for the interconnection of two nonlinear systems described by dynamic <span><math><mrow><mo>(</mo><mi>Ψ</mi><mo>,</mo><mi>Π</mi><mo>,</mo><mi>Υ</mi><mo>,</mo><mi>Ω</mi><mo>)</mo></mrow></math></span>-dissipativity, and are shown to recover several existing results in the literature, including small-gain, passivity indices, static <span><math><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></math></span>-dissipativity, dissipativity with terminal costs, etc. Comparison with the input–output approach to feedback stability analysis based on integral quadratic constraints is also made.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"172 ","pages":"Article 112000"},"PeriodicalIF":4.8000,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824004941","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

Abstract

We propose a general notion of dissipativity with dynamic supply rates for nonlinear systems. This extends classical dissipativity with static supply rates and dynamic supply rates of miscellaneous quadratic forms. The main results of this paper concern Lyapunov and asymptotic stability analysis for nonlinear feedback dissipative systems that are characterised by dissipation inequalities with respect to compatible dynamic supply rates but involving possibly different and independent auxiliary systems. Importantly, dissipativity conditions guaranteeing stability of the state of the feedback systems, without concerns on the stability of the state of the auxiliary systems, are provided. The key results also specialise to a simple coupling test for the interconnection of two nonlinear systems described by dynamic

(Ψ, Π, Υ, Ω)

-dissipativity, and are shown to recover several existing results in the literature, including small-gain, passivity indices, static

(Q, S, R)

-dissipativity, dissipativity with terminal costs, etc. Comparison with the input–output approach to feedback stability analysis based on integral quadratic constraints is also made.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.