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# Solution of Discrete-time Algebraic Riccati Equation

## Solution of Discrete-time Algebraic Riccati Equation

(OP)
Hi

I am trying to solve for X in the DARE (Discrete-time Algebraic Riccati Equation):

A'XA - X - (A'PB+S)*(B'XB+R)^-1*(A'XB+S)' + Q = 0

I know the diagonal matrix (in MATLAB notation) A = [-a 0; 0 a], and B = [b; 0].

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.

Any help is very much appreciated!

Cheers
uncertainwerner

### RE: Solution of Discrete-time Algebraic Riccati Equation

I recommend you read Chapter 13 - Computational Methods for Riccati Equations, in B.N. Datta's "Numerical Methods for Linear Control Systems."

xnuke
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### RE: Solution of Discrete-time Algebraic Riccati Equation

(OP)
I should have mentioned that what I am trying to achieve is to solve the equation analytically instead of numerically.

### RE: Solution of Discrete-time Algebraic Riccati Equation

Continuing education? Most states require 12-14 hours of such to maintain ones P.E. credentials.

Engineering is a continual education...but will agree that this forum really unsuited to class-room assignments.

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