I know that we can determine the roots on the right-half plane by counting the sign changes in the first column. However, I'm unsure how to find the roots on the left-half plane. Is it the same as the right-half plane due to symmetry or am I missing something here?
I think I figured it out. Total number of poles = order of characteristic equation so we can do:
Total number of poles - roots on the right-half plane (# of sign changes in first column) - roots on jw-axis = roots on the left-half plane