An identity concerning controllability observability and coprimeness of linear systems and its applications
Bin ZHOU
Guangren DUAN
Shenmin SONG
摘要：It is shown in this paper that any state space realization (A, b, c) of a given transfer function T(s) = β(s)/α(s)with α(s) monic and dim(A) = deg(α(s)), satisfies the identity β(A) = Qc(A, b)SαQο(A, c) where Qc(A, b) and Qο(A, c) are the controllability matrix and observability matrix of the matrix triple (A, b, c), respectively, and Sα is a nonsingular symmetric matrix. Such an identity gives a deep relationship between the state space description and the transfer function description of single-input single-output (SISO) linear systems. As a direct conclusion, we arrive at the well-known result that a realization of any transfer function is minimal if and only if the numerator and the denominator of the transfer function is coprime. Such a result is also extended to the SISO descriptor linear system case. As an applications,a complete solution to the commuting matrix equation AX = XA is proposed and the minimal realization of multi-input multi-output (MIMO) linear system is considered.
机标关键词：
分类号：TP3(计算技术、计算机技术)
资助基金：国家优秀青年科学家基金(69925308)
论文发表日期：2007-01-01
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：7( 177-183 )
英文信息