# Solve the Riccati eqn symbolically

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END on 4 Mar 2016
Edited: Walter Roberson on 2 Mar 2020
Hi folks
I want to solve the Riccati equation symbolically. For example, I have 4 state variables in Q and 2 inputs in R lqr weights.
Q=diag([q11 q22 q33 q44]);
R=diag([r11 r22]);
The Riccati equation is
A'*P+P*A-P*B*(inv( R ))*B'*P+Q=0
A:4x4 matrix , B:4x2 matrix
I want to solve that equation with respect to "P" matrix variable.
In other words, the answer should be like P=(...) and that should contain the variables q11 q22 q33 q44 and r11 r22. Is there anyone who can help? I appreciate all answers,
Thank you

Walter Roberson on 4 Mar 2016

Walter Roberson on 27 Feb 2020
Unfortunately Internet Archive seems to be having difficulty at the moment, so I have not tracked down an alternative source for this.
Walter Roberson on 28 Feb 2020
Not the link that used to exist, but related topics:
https://www.mathworks.com/help/symbolic/mupad_ref/ode-solve.html (caution: you cannot use this directly inside of MATLAB; you have to use a MuPAD notebook, or you need to use evalin(symengine)
Walter Roberson on 2 Mar 2020
It appears that the original link was probably intended to refer to the discussion that can currently be found at https://groups.google.com/forum/m/#!topic/comp.soft-sys.matlab/lteUP95r03E