Stabilizing solution to the reverse discrete-time Riccati equation: A matrix-pencil-based approach Original Research Article

We derive necessary and sufficient conditions for the existence of the stabilizing solution to the reverse (discrete-time) Riccati equation, a particular type of algebraic Riccati equation which is related to the solution of the discrete-time version of the extended (two-block) Nehari problem. The conditions are expressed in terms of the left-stable deflating subspace of an associated symplectic matrix pencil. In particular, a maximum-phase spectral factorization of the Popov function is obtained under very relaxed conditions imposed on the initial data. It is also proved that under a restrictive additional assumption, the stabilizing solution to the reverse Riccati equation reduces to the antistabilizing solution to the usual (discrete-time) Riccati equation. A reliable numerical algorithm for computing the stabilizing solution to the reverse Riccati equation is also presented, together with formulae for the solution to the extended Nehari problem.