Routh test and covariance control Academic Article uri icon


  • It is well known that positive definiteness of a suitable Lyapunov function is equivalent to the Hurwitz-Routh test. This paper uses the state covariance matrix in a quadratic Lyapunov function to prove the Hurwitz-Routh test and to show a conservation principle relating stability (the characteristic coefficients) to L2 performance. Our proof requires the positive definite test of two matrices approximately half the size of the state, a savings over the usual positive definite test of an nn Lyapunov matrix.

published proceedings

  • Control, theory and advanced technology

author list (cited authors)

  • Skelton, R. E.

complete list of authors

  • Skelton, RE

publication date

  • September 1993