Continued-fraction decomposition of linear systems in the state space
The authors develop a continued fraction decomposition of formal matrix power series \(Z=A_ 1s^{-1}+...+A_ ts^{-t}+...\), \(A_ t\in k^{p\times m}\). The decomposition is interpreted as a certain feedback interconnection of linear systems. If Z is the transfer matrix of a reachable and observable linear system they show that each \(A_ t\) is uniquely associated with a subsystem in the interconnection, moreover a partitioning of the MacMillan degree and of the Kronecker indices is induced. This constitutes a continued fraction canonical form. The maximal (F,G)-invariant subspace contained in ker H can be nicely determined in terms of the decomposition. The results are compared with the decomposition proposed by \textit{P. A. Fuhrmann} [ibid. 3, 263-271 (1983; Zbl 0567.65020).
scientific article; zbMATH DE number 4020932
scientific article