報(bào)告人：劉建州 教授
報(bào)告題目：Accelerated Algorithms for Solving the Unified Algebraic Lyapunov Matrix Equation and Its Application in Stability of Perturbed Systems
報(bào)告時(shí)間：2025年12月20日（周六）下午3：00
報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304報(bào)告廳
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
劉建州，湘潭大學(xué)數(shù)學(xué)與計(jì)算科學(xué)學(xué)院二級(jí)教授、博士生導(dǎo)師。2016.1-2020.1任中國數(shù)學(xué)會(huì)常務(wù)理事，湖南省運(yùn)籌學(xué)會(huì)副理事長，2005.1-2020.11任湖南省數(shù)學(xué)會(huì)常務(wù)理事、秘書長，現(xiàn)任湖南省運(yùn)籌學(xué)會(huì)監(jiān)事長，湖南省數(shù)學(xué)學(xué)會(huì)常務(wù)理事、監(jiān)事。長期從事數(shù)值代數(shù)、線性代數(shù)及其應(yīng)用，線性控制等方面的研究，主持國家自然科學(xué)基金面上項(xiàng)目4項(xiàng)，作為主要成員參加國家重點(diǎn)研發(fā)項(xiàng)目2項(xiàng)，主持部、省級(jí)自然科學(xué)基金10余項(xiàng)，已培養(yǎng)畢業(yè)博士、碩士研究生90余人，在國內(nèi)外重要學(xué)術(shù)期刊《SIMA J. Matrix Anal. Appl.》、《IEEE Transactions on Fuzzy Systems》、《IEEE Transactions on Automatic Control》、《Automatica》《Linear Algebra Appl.》、《Science China Infomation sciences》、《數(shù)學(xué)學(xué)報(bào)》、《數(shù)學(xué)年刊》等發(fā)表術(shù)論文200余篇，其中SCI期刊100余篇。先后獲湖南省自然科學(xué)獎(jiǎng)和湖南省高等教育教學(xué)成果二、三等獎(jiǎng)多項(xiàng)，主編出版《實(shí)用數(shù)學(xué)建模教程》評(píng)為湖南省高等學(xué)校優(yōu)秀教材。
報(bào)告摘要：
This paper establishes several equivalent conditions for a unique positive definite solution of the unified algebraic Lyapunov matrix equation(UALE).
Then, two iterative algorithms for the UALE driven by error precision are pro-posed, which can be accelerated by optimizing the calculation of series terms. The algorithm's convergence, computational complexity, and optimal parameter selection are discussed, supported by a series of numerical experiments that illustrate the effectiveness and superiority of our results.
Finally, by constructing a positive semi-definite matrix and employing matrix-singular inequality, a new robust bound for the unified perturbed system is derived, generalizing some of the existing results. Some numerical experiments demonstrate its practicality and advantage.