Stability Analysis And Sampled-data Control For Switched Affine Neural Networks

Switched neural networks have received more and more attention of researchers in recent years as its widely use in practical application and theoretical significance. Because of the existence of nonlinear activation function in subsystem, the dynamic behavior of switched neural networks becomes more complicated. Therefore, the stability problem of switched neural networks remain to be solved imminently. Based on existing theory of switched linear system, this paper deals with the stability problem of the switched affine neural networks where each subsystem has an affine vector field and proposes a switching rule design method. The main contributions are as follows:Switching rule design problem for a class of switched affine neural networks is investigated in this section. Two kinds of switching rule design method are proposed, which is based on complete system state and system output, respectively. The sliding mode is fully considered by using differential inclusion approach. Combining multiple Lyapunov function approach and Finsler’s lemma, sufficient conditions that guarantee global uniform asymptotic stability of system are established in terms of linear matrix inequality. Finally, a numerical example is used to demonstrate the effectiveness of the obtained results.The stability of a class of switched affine neural networks under sample-data control was studied in this section. The sliding mode may not allow to appear in some situation, thus, we introduce sampled-data control approach. The sampling period of system may change, which makes the study of problem more general. We design the switching rule based on state of sampling points by using single Lyapunov approach, which guarantees the trajectory of switched affine neural networks converges to a certain area, i.e. the global exponential practical stability. The proposed switching rule requests each subsystem running at least one sampling interval time, which avoids the production of the sliding mode effectively. Further, we use multiple Lyapunov function approach and put forward a criteria with less conservativeness. Both of two conclusions are in the form of linear matrix inequality. Two numerical examples are used to illustrate the effectiveness of the results at last.