The Hankel Matrix Solution to a System of Quaternion Matrix Equations
作者单位：College of ScienceGuangxi University for Nationalities
会议名称：《第32届中国控制与决策会议》
会议日期：2020年
学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学]
关 键 词：Quaternion Field Quaternion Matrix Equations Hankel Matrix Kronecker Product Optimal Approximation
摘 要：The solution of matrix equations and the optimal approximation problem play an important role in linear optimal control,parameter identification,structural vibration,aviation and other *** matrix is kind of matrix with special structure and wide *** this paper,the problem of Hankel constraint solution to the system [AXB CXD]=[E F] over quaternion field is *** using the representation of vectors of a Hankel matrix and Kronecker product of matrices,a constrained problem will be transformed into an unconstrained *** the necessary and sufficient conditions for the equations with Hankel solution as well as the expression of general solution are ***,when the solution set is nonempty,by using invariance of Frobenius norm of orthogonal matrix product,the optimal approximation solution with minimal Frobenius norm for a given Hankel matrix is ***,two numerical examples is provided to verify the algorism.