Solving Time-scale algebraic Lyapunov function in Matlab?

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.

Answer 1

[darova]

Here is what i found in MATLAB help

Your equation

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Group 2 and 3 matrices

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Multiply all matrices by

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• I is identity matrix

[Subham Dey]

Thank you!!!!!!!!!

[Subham Dey]

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

[darova]

What does it mean?

[Subham Dey]

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?