{"title":"基于时间尺度矩阵指数函数上限新估算的时间尺度准线性系统稳定性分析","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":"{\"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}","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
摘要
本文基于对时间尺度矩阵指数函数上界的新估计,分析了准线性系统在时间尺度上的稳定性。首先,推导了矩阵指数函数 eA(t,t0) 的一些新的规范上限,其中 A 是回归方阵,t,t0∈T,T 是时间尺度。矩阵指数函数概括了通常的矩阵指数以及矩阵的整数幂。结果表明,与矩阵指数函数规范的现有界限相比,所获得的界限更为精确。其中一个上界随后被用于研究在任意时域上演化的准线性系统的稳定性。
Stability analysis of quasilinear systems on time scale based on a new estimation of the upper bound of the time scale matrix exponential function
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.