Partial realization for singular systems in standard form (Q1590652)

The problem of finding matrices \(A,E,B,C\) for a given sequence \(s=(s_k)^{N-1}_0\) of blocks (partial realization problem) is studied. The matrices should be of the size \(s_i=CE^{N-1-i} A^iB\). The question is whether for any given \(s\) a system of the form \(Ex_{k+1}= Ax_k+ Bu_k\), \(y_k=Cx_k\) exists, for which the state space dimension is equal to the maximum rank of the underlying Hankel matrices. Generally it does not hold. It holds for the block size \(\leq 2\). Realization of discrete-time periodic systems is discussed.