Iterative method of computing the limiting solution of the matrix Riccati differential equation

The paper describes an iterative algorithm for computing the limiting, or steady-state, solution of the matrix Riccati differential equation associated with quadratic minimisation problems in linear systems. It is shown that the positive-definite solution of the algebraic equation PF + F¿P¿PGR¿1G¿P + S = 0, provided that it exists and is unique, can be obtained as the limiting solution of a quadratic matrix difference 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 computational effort with other current techniques for obtaining the limiting solution of the Riccati equation.