{"title":"Relative controllability of neutral delay differential equations on quaternion skew field","authors":"Teng Fu, JinRong Wang","doi":"10.1016/j.cnsns.2024.108557","DOIUrl":null,"url":null,"abstract":"The research focuses on relative controllability of neutral delay differential equations on quaternion skew field (NDQDEs). First, we derive the representation of solutions for NDQDEs by quaternion determining equations and neutral delay quaternion matrix function. Then, the Gram criterion of relative controllability for NDQDEs in different cases is given with the help of the representation of solutions. By the analogy of Cayley–Hamilton theorem, the rank criterion of relative controllability is obtained. The complete characterization of quaternion control functions is obtained by a special right inverse matrix and shifted Legendre polynomials. Besides, we discuss the relative controllability of weakly nonlinear NDQDEs. Finally, we provide examples to verify the theoretical results.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"11 1","pages":""},"PeriodicalIF":3.4000,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.cnsns.2024.108557","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The research focuses on relative controllability of neutral delay differential equations on quaternion skew field (NDQDEs). First, we derive the representation of solutions for NDQDEs by quaternion determining equations and neutral delay quaternion matrix function. Then, the Gram criterion of relative controllability for NDQDEs in different cases is given with the help of the representation of solutions. By the analogy of Cayley–Hamilton theorem, the rank criterion of relative controllability is obtained. The complete characterization of quaternion control functions is obtained by a special right inverse matrix and shifted Legendre polynomials. Besides, we discuss the relative controllability of weakly nonlinear NDQDEs. Finally, we provide examples to verify the theoretical results.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
