Reza Lavaei, Frank Cao, Amy K. Strong, Leila J. Bridgeman
{"title":"Iterative, local, small-signal L2 stability analysis of nonlinear constrained systems","authors":"Reza Lavaei, Frank Cao, Amy K. Strong, Leila J. Bridgeman","doi":"10.1016/j.sysconle.2025.106065","DOIUrl":null,"url":null,"abstract":"<div><div>This paper provides a method to analyze the local, small-signal <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-gain of control-affine nonlinear systems on compact sets via iterative semi-definite programs. First, a continuous piecewise affine storage function and the corresponding upper bound on the local <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-gain are found on a bounded, compact set’s triangulation. Then, to ensure that the state does not escape this set, a continuous piecewise affine barrier function is found that is robust to small-signal inputs. Local, small-signal <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> stability then holds inside each sublevel set of the barrier function inside the set where the storage function was found. The method’s effectiveness is shown in a numerical example.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"199 ","pages":"Article 106065"},"PeriodicalIF":2.1000,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691125000477","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper provides a method to analyze the local, small-signal -gain of control-affine nonlinear systems on compact sets via iterative semi-definite programs. First, a continuous piecewise affine storage function and the corresponding upper bound on the local -gain are found on a bounded, compact set’s triangulation. Then, to ensure that the state does not escape this set, a continuous piecewise affine barrier function is found that is robust to small-signal inputs. Local, small-signal stability then holds inside each sublevel set of the barrier function inside the set where the storage function was found. The method’s effectiveness is shown in a numerical example.
期刊介绍：
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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