Solution:

In control system theory, the Routh?Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time invariant (LTI) control system. The importance of the criterion is that the roots of the characteristic equation of a linear system with negative real parts represent solutions of the system that are stable (bounded). Thus the criterion provides a way to determine if the equations of motion of a linear system have only stable solutions, without solving the system directly.