Global exponential stability of a class of impulsive neural networks with unstable continuous and discrete dynamics

This paper deals with global exponential stability of a class of impulsive neural networks whose continuous and discrete dynamics are unstable. Assuming that the impulsive neural network under consideration can be decomposed into two lower order impulsive systems, a time-varying weighted Lyapunov function associated with the impulse time sequence is introduced for stability analysis. A novel global exponential stability criterion is derived in terms of linear matrix inequalities (LMIs). By employing the newly obtained stability criterion, a sufficient condition on the existence of a reduced-order impulsive controller is derived. Unlike the previous results concerning impulsive control, the proposed reduced-order impulsive controller only exerts the impulses on a partial set of the state vector. Moreover, the controller gain matrices can be achieved by solving a set of LMIs. Finally, four illustrative examples are given to show the effectiveness of the developed techniques and results.