# Analytical solution of Discrete-time Algebraic Riccati Equation

1. Oct 7, 2014

### wavingerwin

1. The problem statement, all variables and given/known data
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!

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

3. 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.

2. Oct 12, 2014