A new solution of the discrete algebraic Riccati equation

A theoretically interesting and computationally attractive solution of the discrete algebraic Riccati equation is presented. The solution is based on Luenberger's canonical representation of controllable multivariable systems and a result due to Vaughan whereby the solution is written in terms of the eigenvectors of a corresponding Hamiltonian matrix. Concise expressions for these eigenvectors are developed in terms of a much simpler reduced Hamiltonian system.