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There is a matrix equation A1-A2X+XA3-XA4X=0. where, A1,A2,A3,A4 all are [2X2] matrix. Then how to find X which is also a [2X2] matrix?

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Matt J
Matt J 2022-3-15
编辑：Matt J 2022-3-15

1 个投票

You can try fsolve, but you will need a good initial guess, X0.
X=fsolve(@(X) A1-A2*X+X*A3-X*A4*X, X0)

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Torsten
Torsten 2022-3-15
Any classification of the equation possible (e.g. Riccati) ?
I guess: no, but perhaps someone else has more experience.
Sam Chak
Sam Chak 2022-3-15
It does look like an algebraic Riccati equation to me. It is usually encountered in the time-invariant Linear-Quadratic Regulator (LQR) problem.
https://en.wikipedia.org/wiki/Linear%E2%80%93quadratic_regulator
Conventionally, it can be solved through the matrix decomposition procedure called Schur, named after a Russian mathematician.
https://www.mathworks.com/help/matlab/ref/schur.html
Can also try solving the matrix equation using the LMI Solver (a very powerful and versatile tool for solving a number of problems). But the formulation part can be quite tricky and frustrating is the matrices are very large.
https://www.mathworks.com/help/robust/lmis.html
Torsten
Torsten 2022-3-15
编辑：Torsten 2022-3-15
Since A2 is not equal to -A3.', I couldn't bring it into the Riccati form MATLAB's idare expects.
Do you have a suggestion ?
Sam Chak
Sam Chak 2022-3-15
Ah! I have forgotten there were care and dare in the olden days.
Let's wait for @Kallol Chatterjee to clarify if .
Kallol Chatterjee
Kallol Chatterjee 2022-3-16
The Problem is not a Riccati equation type. Actually on the system equation there is no condition of symetricity. I am converting the system into slow and fast response. For that I need to change the coordinate transformation. To solve this transformation I need this solution.
Kallol Chatterjee
Kallol Chatterjee 2022-3-16
There is no relation between A2 and A3.
Kallol Chatterjee
Kallol Chatterjee 2022-3-16
@Matt J Thanks for helping me. It finds the solution.

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