Qualitative Analysis and Controllability
of Quaternion-Valued Systems
报告专家：王锦荣 教授（贵州大学）
报告时间：10月17日（周六）下午14:00-14:45
报告地点：数学学院西303
报告摘要：
The report introduces the origin, application and characteristics of quaternions. For the quaternion-valued delay difference system, by introducing the appropriate quaternion discrete matrix delay exponential, the exact solution of the linear delay difference system is derived, and the necessary and sufficient conditions for the controllability of the linear system are given. The concept of a quaternion reachable division ring is introduced. By using the left linear independence of quaternion vectors, the difficulty caused by the fact that the transpose of the product of matrices in the quaternion sense is not equal to the product of the transposed matrices is overcome, and the rank criterion for the controllability of linear system is established. For the quaternion-valued delay differential system, by introducing the appropriate quaternion delay matrix exponential function, the exact solution of the linear delay differential system is derived, and the necessary and sufficient conditions for the controllability of the linear system and the sufficient conditions for the controllability of the nonlinear system are given. The concept of the maximal right linearly independent group of quaternion vectors is proposed, which overcomes the challenge posed by the failure of the Cayley-Hamilton theorem to hold in the sense of quaternions, and the rank criterion for the controllability of the linear system is established.
专家简介：
王锦荣，二级教授、贵州大学博士生导师。贵州省科学技术厅党组成员、副厅长，国家天元数学西南中心贵州基地主任。入选国家百千万人才工程，并被授予“有突出贡献中青年专家”荣誉称号，是国务院特殊津贴获得者、教育部科技委数理学部委员、教育部大学数学课程教指委委员、中国数学会常务理事、国家天元数学西南中心贵州基地主任、宝钢优秀教师、贵州省核心专家、“贵州科技创新奖”个人奖获得者、贵州省最美科技工作者、贵州省五一劳动奖章获得者。主持国家自然科学基金5项，在Springer、Elsevier、IOP等出版专著6部，以第一完成人身份获贵州省自然科学一等奖1项和研究生教学成果特等奖2项，已在Journal of Functional Analysis、SIAM Journal on Control and Optimization、Journal of Differential Equations、IEEE Transactions on Automatic Control、Physics of Fluids等杂志发表论文多篇。
邀请人：张旭
