Routh test and covariance control
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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.
