Improved Robust Stability Criteria for Delayed Cellular Neural Networks via the LMI Approach

Uniqueness and robust exponential stability are analyzed for a class of uncertain cellular neural networks with time-varying delays. By dividing the variation interval of the time delay into two subintervals with equal length, a novel Lyapunov-Krasovskii functional is introduced. Using the free-weighting matrix method, a new delay-dependent stability criterion is obtained, which is less conservative than some previous literature. Since the result is presented in terms of linear matrix inequalities, the condition is easy to be verified. Finally, an example is given to illustrate the effectiveness of our proposed method.

I. Introduction

It is well known that time delays always appear in many neural networks as a source of instability and bad performance. These networks include Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. Moreover, it has been shown that applications of neural networks heavily rely on the dynamical behaviors of the networks. Therefore, the stability analysis problem of neural networks with time delays has attracted a large amount of research interest, and many sufficient conditions have been proposed to guarantee the asymptotic or exponential stability for the neural networks [1]–[20]. On the other hand, the uncertainties in various neural networks are unavoidable due to modeling errors, measurement errors, linearization approximations, and so on. Hence, the problem of robust stability analysis of uncertain neural networks with time delays has extensively been investigated recently [7]–[9], [15]–[18].