Solving Time-scale algebraic Lyapunov function in Matlab?

2020 2 27
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更新时间：2020 2 29
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I wish to solve the following equation on Matlab:
A^(T)P + P A + µA^(T)P A = −M,
where A is known matrix and M is a positive-definite matrix as well as µ is a known constant. P is a matrix to be found.
Note: I looked into the lyap function and think of it is as a some kind extension of it. I am not asking for solution but any hints would be highly helpful.

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darova
darova 2020-2-27
编辑：darova 2020-2-27

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Here is what i found in MATLAB help
Your equation
Group 2 and 3 matrices
Multiply all matrices by
  • I is identity matrix

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Subham Dey
Subham Dey 2020-2-28
Hi,
However I need to ensure that P is a positive definite matrix given A is Hurwitz in nature. I apologize, I should have mentioned before.
Regard
Subham Dey
Subham Dey
Subham Dey 2020-2-29
If all the eigen values of A have negative real parts then the matrix A is called Hurwitz. If matrix A is Hurwitz then the solution of Lyapunov equation gives a positive definite matrix P for a positive definite matrix Q (P=lyap(A,Q)). However, I am unsure how to the get the solution of Sylvester equation to be positive definite?

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