【摘要】 基于求线性矩阵方程约束解的修正共轭梯度法,针对源于低增益反馈设计和时滞控制系统中的一类参量离散代数Riccati方程,建立求其非零对称解的Newton-MCG算法和非精确Newton-MCG算法以及求其可逆对称解的T-MCG算法.(非精确)Newton-MCG算法仅要求Riccati方程存在非零对称解,对系数矩阵等没有附加限定,但所得对称解不能保证可逆性或正定性;在系数矩阵满足可控性等条件下,由T-MCG算法所得对称解是正定的.数值算例表明,两类迭代算法是有效的.更多还原

【Abstract】 This paper focuses upon iterative algorithms for the nonzero symmetric solutior of discrete-time algebraic Riccati equation arising from low gain feedback design and timt delay control system.Based on the modified conjugate gradient method,the(inexact’Newton-MCG algorithm and T-MCG algorithm are proposed.The(inexact) Newton-MCG algorithm has no other limits to coefficient matrices except for the existence of nonzerc symmetric solution,while T-MCG algorithm demands the existence of invertible symmetric solution.Particularly,the solution derived from T-MCG algorithm is positive definite undei suitable conditions such as controllabilities of relative coefficient matrices,but the solutior from(inexact) Newton-MCG algorithm is not necessarily.Numerical results illustrate the efficiency of the above algorithms.更多还原