Reduced-Order Solution of the Weakly Coupled Matrix Difference Riccati Equation

This paper presents a new method to get the solution of the weakly coupled matrix difference Riccati equation by solving two reduced order linear difference equations. The order reduction is achieved by using a decoupling transformation applied to the Hamiltonian matrix of a weakly coupled discrete linear-quadratic control problem. Since the decoupling transformation can be obtained, up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for solving weakly coupled difference Riccati equation.