Delayed state-feedback control for stabilization of neural networks with leakage delay

This paper mainly deals with the problem of designing delayed state-feedback controller for neural networks with leakage delay. By constructing an appropriate Lyapunov-Krasovskii functional including double integral terms having two different exponential decay rates and utilizing linear matrix inequality (LMI) technique with the help of slack variables, some sufficient conditions for globally exponential stabilization results are obtained by designing of delayed state-feedback controller. The novelty of this paper includes: (i) although many papers dealt with dynamics of neural networks with leakage delay, there is little work on design of feedback controller. Even there is almost no result that deals with the delay-feedback controller for such delay systems, which is the main motivation of this paper; (ii) the derived delay-dependent stability criteria establish the relationship between leakage delay and time delay in the feedback term, which can be easily checked via the MATLAB LMI toolbox; (iii) we consider the general case that the control term is given in the form of Bu, where B is an n×m real matrix. Such case is more difficult to handle than the special case that B is unit matrix. It indicates that the controller can be used in all states or in some states by proper selection of the matrix B. The effectiveness of the proposed method in this paper is illustrated via numerical examples.