Analytical solution of Discrete-time Algebraic Riccati Equation

[wavingerwin]

Homework Statement

Solve for [itex]X[/itex] in the DARE (Discrete-time Algebraic Riccati Equation) analytically. A is diagonal [itex]A = [-a\;0; 0 \;a][/itex], and [itex]B = [b; 0][/itex] (in MATLAB notation).

Any help is very much appreciated!

Homework Equations

The DARE is given as
[itex]A'XA - X - (A'PB+S)(B'XB+R)^{-1}(A'XB+S)' + Q = 0[/itex]

The Attempt at a Solution

I have tried looking and reading and the closest I get is to utilise the Hamiltonian / Sympletic matrix. However, I have no clue in proceeding forward.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?