Stability Of Cellular Neural Network Based On Matrix Inequality Research And Circuit Implementation

Cellular neural networks is a class nonlinear simulated dynamical system, its structure is consistent and its dimension can be extended indefinitely, of which dynamic characteristics mainly include chaos, periodicity, approximate periodicity and stability. Stability of cellular neural networks has been widely used in many areas, including pattern recognition, image processing, global optimization and so on.Global asymptotic stability is one of the focus in the study of stability of cellular neural networks, on which a certain depth of analysis and research is carried on in this paper, the main work is carried out as follows:(1) Preferable Lyapunov-Krasovskii functional related to the system equations is constructed and Lyapunov stability theorem is utilized to analyze, new stability criterion with different forms of matrix inequalities are obtained. The stability criterion mostly come from system’s own template, to some extent, it avoids the interference of the introduction of external parameters on the system. Under the premise of showing good stability effect, this method can reduce costs when the system model is applied to the actual.(2) Quadratic theory is used to study the global asymptotic stability of cellular neural networks without delays. The obtained criterion can not only be applied to arbitrary dimensional systems, but also reduced matrix dimension of existing criterion from2n to n. Not only does it effectively reduce the computational complexity and checking standards of sufficient criteria, but also reduce the conservatism of criteria under original better verifiable conditions. Cellular neural networks circuit by modular design combined with the numerical simulation of stability is used to do the analog circuit simulation experiment, and they have same results.(3) The negative impact of time delay on the stability of cellular neural networks is fully considered. Global asymptotic stability of a class of open-dimension cellular neural networks with time delay is researched. The stability condition is with the form of linear matrix inequalities representation. The criterion possesses delay-independent properties, which effectively prevents the interference of the delay on the stability. Based on the circuit design of system without delays, circuit module with delays is increased and a good simulation result of stability of the circuit with delays is received.(4) Chaos synchronization system consists of two types of cellular neural networks is looked as a new cellular neural network system. After analysis of the stability of the two types of cellular neural networks, a similar approach combined with synchronous controller design is used to get a set of stability conditions of the new system, which is synchronization condition of chaotic systems with different structures composed of these two different types of cellular neural networks. This synchronous controller is achieved by Simulink circuit simulation.