The four-block Adamjan–Arov–Krein problem for discrete-time systems Original Research Article

We consider the problem of approximating in H∞ norm a given discrete inverse-time stable system (possibly improper) image by a discrete-time system S with no more than r poles outside the unit disk (possibly at infinity) such that image Here rgreater-or-equal, slanted0 is an integer and γ>0 is a prescribed tolerance. If r=0, this is the four-block Nehari problem while if we consider the “one block case” where T=T11 we obtain the well-known Hankel norm approximation problem. The theoretical developments are based on a frequency domain signature condition while the class of solutions is constructed in state-space in terms of the solutions to two Riccati equations.