Set-valued derivative and Lyapunov method for full-range cellular neural networks

The paper proposes an alternate definition of set-valued derivative, with respect to that in a previous paper, for computing the evolution of a (candidate) Lyapunov function along the solutions of a class of differential variational inequalities (DVIs). The class of DVIs is of interest in that it includes as a special case the dynamics of full-range (FR) cellular neural networks (CNNs). The usefulness of the new definition is discussed in the context of a generalized Lyapunov method for addressing stability and convergence of solutions of DVIs and FR-CNNs.