{"title":"Stability analysis of quasilinear systems on time scale based on a new estimation of the upper bound of the time scale matrix exponential function","authors":"","doi":"10.1016/j.jfranklin.2024.107312","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the stability of quasilinear systems on time scale is analyzed based on a new estimation of the upper bound of the time scale matrix exponential function. First, some new upper bounds for the norm of the matrix exponential function <span><math><mrow><msub><mrow><mi>e</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span> are derived, where <span><math><mi>A</mi></math></span> is a regressive square matrix, <span><math><mrow><mi>t</mi><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mi>T</mi></mrow></math></span>, <span><math><mi>T</mi></math></span> being a time scale. The matrix exponential function generalizes the usual matrix exponential as well as the integer power of a matrix. It is shown that the obtained bounds are more accurate compared to the existing bounds of the norm of the matrix exponential function. One of the upper bounds is then used for stability investigation of quasilinear systems evolving on arbitrary time domains.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003224007336","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the stability of quasilinear systems on time scale is analyzed based on a new estimation of the upper bound of the time scale matrix exponential function. First, some new upper bounds for the norm of the matrix exponential function are derived, where is a regressive square matrix, , being a time scale. The matrix exponential function generalizes the usual matrix exponential as well as the integer power of a matrix. It is shown that the obtained bounds are more accurate compared to the existing bounds of the norm of the matrix exponential function. One of the upper bounds is then used for stability investigation of quasilinear systems evolving on arbitrary time domains.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.