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This paper develops a Lyapunov approach for studying convergence and stability of a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs describe the dynamics of a general system evolving in a compact convex subset of the state space. In particular, they include the dynamics of the full-range (FR) model of cellular neural networks (CNNs), which is characterized by hard-limiter nonlinearities with vertical segments in the i-v characteristic. The approach is based on the following two main tools: 1) a set-valued derivative, which enables to compute the evolution of a Lyapunov function along the solutions of the DVIs without involving integrations, and 2) an extended version of LaSalle's invariance principle, which permits to study the limiting behavior of the solutions with respect to the invariant sets of the DVIs. Then, this paper establishes conditions for convergence (complete stability) of DVIs in the presence of multiple equilibrium points (EPs), global asymptotic stability (GAS), and global exponential stability (GES) of the unique EP. These conditions are applied to investigate convergence, GAS, and GES for FR-CNNs and some extended classes of FR-CNNs. It is shown that, by means of the techniques developed in this paper, the analysis of convergence and stability of FR-CNNs is no more difficult than that of the standard (S)-CNN5. In addition, there are significant cases, such as the symmetric FR-CNNs and the nonsymmetric FR-CNNs with a Lyapunov diagonally stable matrix, where the proof of convergence or global stability is much simpler than that of the S-CNNs. [ABSTRACT FROM AUTHOR]

Lyapunov functionals and Lyapunov functions coupled with the Razumildiin technique are still the most popular tools in studying the stability of large-scale retarded nonlinear systems. However, it is generally difficult to construct Lyapunov functionals or functions that satisfy the strong conditions required in the classical stability theory. In this paper, we show that for some delay differential systems such as additive neural networks with delays, we can weaken the condition that the Lyapunov functional or function is positive definite, by using the equivalence between the state stability and the output stability. We apply our general theory to obtain some new stability conditions for cellular neural network models. It is represented that it is easy to construct Lyapunov functionals or functions satisfied conditions of our theorems. [ABSTRACT FROM AUTHOR]

Cellular neural networks (CNNs) are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium-point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNNs, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements. [ABSTRACT FROM AUTHOR]