A nonrecursive algebraic solution for the discrete Riccati equation

Equations for the optimal linear control and filter gains for linear discrete systems with quadratic performance criteria are widely documented. A nonrecursive algebraic solution for the Riccati equation is presented. These relations allow the determination of the steady-state solution of the Riccati equation directly without iteration. The relations also allow the direct determination of the transient solution for any particular time without proceeding recursively from the initial conditions. The method involves finding the eigenvalues and eigenvectors of the canonical state-costate equations.