Stability analysis of static recurrent neural networks with interval time-varying delay

Keywords: Delay-dependent stability Interval time-varying delay Static recurrent neural network Linear matrix inequality a b s t r a c t The problem of stability analysis of static recurrent neural networks with interval time-varying delay is investigated in this paper. A new Lyapunov functional which contains some new double integral and triple integral terms are introduced. Information about the lower bound of the delay is fully used in the Lyapunov functional. Integral and double integral terms in the derivative of the Lyapunov functional are divided into some parts to get less conservative results. Some sufficient stability conditions are obtained in terms of linear matrix inequality (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method. During past several decades, recurrent neural networks have been applied in many areas such as speech recognition, handwriting recognition, optimization problem, model identification and automatic control [1,2]. Although neural networks can be implemented by very large scale integrated circuits, there inevitably exist some delays in neural networks due to the limitation of the speed of transmission and switching of signals. It is well known that time-delay is usually a cause of instability and oscillations of recurrent neural networks. Therefore, the problem of stability of recurrent neural networks with time-delay is of importance in both theory and practice. Many results on this topic have been obtained which can be classified into delay-dependent ones and delay-independent ones. Since delay-dependent stability conditions are usually less conservative than delay-independent ones, much attention has been put into developing some less conservative delay-dependent stability conditions [3–24]. Neural networks can be classified into two categories, that is, static neural networks and local field networks. In static neural networks, neuron states are chosen as basic variables. While in local field networks, local field states are chosen as basic variables. It has been proved that these two kinds of neural networks are not always equivalent [25]. Compared with rich results for local field networks, results for static neural networks are much more scare. To mention a few, stability of static recurrent neural networks with constant time-delay was investigated in [26] where new delay-dependent stability criteria were established in the terms of LMI using delay-partitioning approach and Finsler's lemma. By introducing some slack matrices, delay-dependent stability conditions for static recurrent neural networks with time-varying delay were obtained and expressed as LMIs [27]. By constructing a new Lyapunov functional and using s-procedure, both …