Solution of kalman-yakubovich conjugate matrix equation

[Zaryab]

Let the matrices ?∈??×? and ?∈??×? be
given. If the matrix ?? is Schur stable, then the unique solution
of the matrix equation ?−???? = ? is expressed as
? = ∏(?, ?, ??) [?̃
?? (????)]−1
which is a polynomial of matrices ? and ?.

 

[Deleted member 4993]

Let the matrices ?∈??×? and ?∈??×? be
given. If the matrix ?? is Schur stable, then the unique solution
of the matrix equation ?−???? = ? is expressed as
? = ∏(?, ?, ??) [?̃
?? (????)]−1
which is a polynomial of matrices ? and ?.

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[Romsek]

The question as written is a mess.

Is AT supposed to be [MATH]A^T[/MATH]
what is AHAT? Is that [MATH]\hat{A}[/MATH], in which case what does that mean?
is it [MATH]A^H A^T[/MATH] i.e. the product of the Hermitian and the Transpose?

Throw us a bone here.

 

[Deleted member 4993]

View attachment 23571

This is a corollary. Are you looking for a way to prove this corollary?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.