in finding riccati solution of(adsbygoogle = window.adsbygoogle || []).push({});

A*X+A'*X+X*W*X+Q that is

X which stabilises A+W*X(real parts of eigen values are <0) ,it’s existence can

Found out by

Eigen values of Hamiltonian matrix H given by

H MATRIX=

!A W!

!Q -A!

because we have the relation

EIGEN VALUE OF H ARE GIVEN BY= EIGENVALUES OF (A+W*x)& - (A+W*x);

In text it is stated as if there is no eigen values of H are on imaginary axis then X exists

Means it can have in real parts of ( eigen values can be >0)

This can be possible

If A+W*x has negative real parts

And also A+W*x has positive real parts in which it is un stable

If it is so how can we say that just H matrix not having eigen values on imaginary axis is

Sufficient for X toexist

Can any one explain me about this

Thanking you

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# Hamaltonian of system

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