In mathematics, the gives a test to determine whether all roots of a given polynomial lie in the left half-plane. Polynomials with this property are called Hurwitz stable polynomials. is important in dynamical systems and control theory because the characteristic polynomial of the differential equations of a stable linear system has roots limited to the left half plane (negative eigenvalues). Thus, the theorem provides a test to determine whether a linear dynamical system is stable without solving the system. The Routh-Hurwitz theorem was proved in 1895 , and it was named after Edward John Routh and Adolf Hurwitz. EXERCISE Exercise 3.1: Procedure: a) Enter the program in the editor window. b) Execute the Program (See Appendix) c) Enter the coefficients of characteristic equation in the command window. The Routh matrix is obtained in the command window