The variable gradient method for generating liapunov functions
- 1 September 1962
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry
- Vol. 81 (4) , 203-210
- https://doi.org/10.1109/tai.1962.6371818
Abstract
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.Keywords
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