The generalised discrete algebraic Riccati equation arising in LQ optimal control problems: Part I

A geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati equation arising from the classic infinite-horizon linear quadratic (LQ) control problem and the output-nulling and reachability subspaces of the underlying system. This analysis reveals the presence of a subspace that plays a crucial role in the solution of the related optimal control problem.