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Hamaltonian of system

  1. Jul 6, 2004 #1

    gs

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    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) ,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
     
  2. jcsd
  3. Jul 12, 2004 #2

    gs

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    this relation of eigen values of h and (a,w)is valid for x stable hence it is sufficient
     
  4. Jul 14, 2004 #3

    Tom Mattson

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    Staff Emeritus
    Science Advisor
    Gold Member

    I'm a little confused. What are the dimensions of these quantities? Are they matrices? Vectors? Scalars?

    Is there some significance to the symbols & and ; here?
     
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