Solution of Discrete-time Algebraic Riccati Equation

[uncertainwerner]

Hi

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

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

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

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

 

[xnuke]

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

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IRstuff]

Matlab Control System Toolbox has a solver for DARE:

http://www.mathworks.com/help/control/ref/dare.html?refresh=true

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

Of course I can. I can do anything. I can do absolutely anything. I'm an expert!

 

[uncertainwerner]

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

 

[IRstuff]

Is this for school? Student posting is not allowed.

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

Of course I can. I can do anything. I can do absolutely anything. I'm an expert!

 

[hacksaw]

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.