ITERATIVE METHOD OF COMPUTING THE LIMITING SOLUTION OF THE MATRIX RICCATI DIFFERENTIAL EQUATION.

An iterative algorithm for computing the limiting, or steady-state, solution of the matrix Riccati differential equation associated with quadratic minimization problems in linear systems is described. It is shown that the positive-definite solution of the algebraic equation PF plus F prime P - PGR** minus **1G prime P plus S equals O, provided that it exists and is unique, can be obtained as the limiting solution of a quadratic matrix different equation that converges from any nonnegative definite initial condition. The algorithm is simple, and, at least for moderate dimensions of the solution matrix, competitive in computatonal effort with other current techniques for obtaining the limiting solution of the Riccati equation.