Structure-preserving numerical algorithm for solving discrete-time LMI and DARS

We present a numerical algorithm to solve a discrete-time linear matrix inequality (LMI) and discrete-time algebraic Riccati system (DARS). With a given system ( A , B , C , D ) we associate a para-hermitian matrix pencil. Then we transform it by an orthogonal transformation matrix into a block-triangular para-hermitian form. Under either of the two assumptions (1) matrix pair ( A , B ) is controllable or (2) matrix pair ( A , B ) is reachable and ( A , B , C , D ) is a left invertible system, we extract the solution of LMI and DARS by the entries of the orthogonal transformation matrix.