Stability Analysis Of Fuzzy Cellular Neural Networks With Time-varying Delays

Since 1996, fuzzy cellular neural networks (Fuzzy Cellular Neural Networks, FCNNs) were firstly investigated by T. Yang and L. Yang, have been extensively studied both in theory and applications, including dynamical image processing, signal process, etc. In many practical applications, we always require that the system could reach a stable equilibrium under contain conditions. Therefore, the study on stability of fuzzy cellular neural networks is of great significance.In real world, time delay and random factors always unavoidably occur. The time delay often destroy a stably system, at the same time, the presence of random noise makes systems analysis and control design much more complicated. In this dissertation, the problem of stability for fuzzy cellular neural networks with time-varying delays and stochastic fuzzy cellular neural networks with time-varying delays is investigated. The dissertation contains six chapters:In Chapter 1, a summary of neural networks is outlined; then, time delay phenomenon on the stability of neural networks is discussed. Finally, the recent results on stability of fuzzy cellular neural networks are presented, and two fuzzy cellular neural networks models are proposed.In Chapter 2, some related concepts and theorems on stability theory of deterministic and stochastic delay systems are introduced, and linear matrix inequality technique is presented.In Chapter 3, global exponential stability of fuzzy cellular neural networks with time-varying delays is investigated. To decreasing the conservativeness of the obtained results, we construct a suitable Lyapunov-Krasovskii functional and use the integral matrix inequality, a novel delay-dependent stability criterion is derived and presented in terms of a linear matrix inequality. Finally, some numerical examples are shown that results in this chapter are better than some results of the existing literature.In Chapter 4, the problem of global asymptotic stability in the mean square for stochastic fuzzy cellular neural networks with time-varying delays is studied. By constructing a newly proposed Lyapunov-Krasovskii functional and using stability theory of stochastic delayed systems, a novel delay-dependent stability criterion is derived and presented in terms of a linear matrix inequality. Finally, an illustrate example is given to verify the feasibility and usefulness of the proposal result.In Chapter 5, global exponential stability in the mean square of stochastic fuzzy cellular neural networks with time-varying delays is discussed. By constructing a new Lyapunov-Krasovskii functional and using stability theory of stochastic delayed systems, a novel delay-dependent stability criterion is derived, and the result is presented in terms of a linear matrix inequality. Finally, an illustrate example is given to verify the effectiveness and feasibility of the proposal result.Lastly, we summarize the major work in this dissertation and point out some directions of the development of neural networks.