LOWER BOUNDS FOR THE TRACE OF THE SOLUTION OF THE DISCRETE ALGEBRAIC RICCATI EQUATION

Abstract

This note suggests two lower bounds for the trace of the solution of the discrete algebraic Riccati equation (DARE). It is shown that in many cases, the trace bounds of this note are tighter than those in the literature and greater than the trace of the state weighting matrix even when the system matrix is singular. The results are illustrated through an example.