Formulation of a definite class of Lyapunov functions

The process presented in this correspondence will generate a Lyapunov function with a negative-definite time derivative for all systems in phase variable form which satisfy the conditions of Lyapunov's first method and one extra continuity condition. For an
n
th-order system, in order to determine a set of
n - 1
constants, the method requires a calculation of one inverse of a matrix which is related to the Routh-Hurwitz matrix. The remainder of the constants and the desired Lyapunov function are found by using recursive formulas. Except when the inverse does not exist, the method generates a scalar function which will determine instability by Chetaèv's theorem for those systems where the first method applies. The process is then extended to the case where the first method fails.