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Hamaltonian of system

by gs
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gs
#1
Jul6-04, 07:02 AM
P: 6
in finding riccati solution of

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

X which stabilises A+W*X(real parts of eigen values are <0) ,itís 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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gs
#2
Jul12-04, 12:59 PM
P: 6
this relation of eigen values of h and (a,w)is valid for x stable hence it is sufficient
Tom Mattson
#3
Jul14-04, 02:34 PM
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Quote Quote by gs
in finding riccati solution of

A*X+A'*X+X*W*X+Q that is
I'm a little confused. What are the dimensions of these quantities? Are they matrices? Vectors? Scalars?

EIGEN VALUE OF H ARE GIVEN BY= EIGENVALUES OF (A+W*x)& - (A+W*x);
Is there some significance to the symbols & and ; here?


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