The variable gradient method for generating liapunov functions

A logical and systematic method of generating Liapunov functions for determining stability of nonlinear autonomous systems is introduced. The method is based upon the assumption of a variable gradient function from which both V and V may be determined. The n-un-known elements of each of the n-components of the variable gradient are determined from constraints on V and n(n¿1)/2 generalized curl equations. The type of V-functions produced include those involving higher order terms, one or more integrals, and terms with more than two state variables as factors. Nontrivial examples of the above cases are included.