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)(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)(A,B) is controllable or (2) matrix pair (A,B)(A,B) is reachable and (A,B,C,D)(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.