Stability analysis of Lagrange neural networks

By redefining multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse the method dedicated to equality constraints for constructing Lagrange neural networks. The local stability of the Lagrange neural networks is proved rigorously with the first Liapunov approximation principle. The stability in the large is discussed based on the LaSalle invariance principle.