Analytical solution of Discrete-time Algebraic Riccati Equation

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SUMMARY

The forum discussion focuses on solving the Discrete-time Algebraic Riccati Equation (DARE) analytically, specifically with a diagonal matrix A defined as A = [-a; 0; 0; a] and a matrix B = [b; 0] in MATLAB notation. The DARE is expressed through the equation A'XA - X - (A'PB + S)(B'XB + R)^{-1}(A'XB + S)' + Q = 0. The user seeks assistance in utilizing the Hamiltonian/Symplectic matrix approach to progress in their solution. The discussion highlights the need for clarity and further insights to advance the analytical solution process.

PREREQUISITES
  • Understanding of Discrete-time Algebraic Riccati Equation (DARE)
  • Familiarity with MATLAB for matrix representation
  • Knowledge of Hamiltonian and Symplectic matrices
  • Basic concepts of Linear Algebra and matrix operations
NEXT STEPS
  • Research analytical methods for solving Discrete-time Algebraic Riccati Equations
  • Explore MATLAB functions for matrix manipulation and solving equations
  • Study Hamiltonian and Symplectic matrix theory in detail
  • Investigate numerical solutions for DARE using MATLAB toolboxes
USEFUL FOR

Students and researchers in control theory, applied mathematics, and engineering disciplines who are working on solving Discrete-time Algebraic Riccati Equations and require a deeper understanding of analytical methods and MATLAB applications.

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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