Analytical solution of Discrete-time Algebraic Riccati Equation

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The discussion focuses on solving the Discrete-time Algebraic Riccati Equation (DARE) analytically with a specific diagonal matrix A and vector B. The equation is presented, highlighting the challenge in finding the solution for X. The user has attempted to utilize the Hamiltonian/Symplectic matrix approach but is uncertain about the next steps. There is a request for additional insights or rephrasing the post to attract more responses. The need for clarity and further information in tackling the DARE is emphasized.
wavingerwin
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Homework Statement


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

Any help is very much appreciated!

Homework Equations


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

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.
 
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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?
 

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