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
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?