Novel Switching Laws for Switched Nonlinear Time-Delay Systems and Applications to Neural Networks

This article addresses the switching law design problem for switched nonlinear time-delay systems (SNTDSs). The existing switching laws, such as dwell time, average dwell time (ADT), and mode-dependent ADT (MDADT), depict the switching frequency by linear functions of switching interval length, which may insufficiently characterize the switching numbers and features of SNTDSs. To effectively ensure the system stability of SNTDSs and relax the conservatism of stability criteria, two novel switching laws, average switching density and mode-dependent average switching density (MDASD), are first proposed to illustrate the switching frequency of SNTDSs. Meanwhile, under the new switching laws, by constructing the proper multiple Lyapunov-Razumikhin functions, relaxed integral inequalities, and the trajectory-based approach, stability criteria are presented for SNTDSs, which can encompass and include certain aspects of prior research. Moreover, we apply the new switching laws and theoretical results to switched neural networks. Ultimately, we present two examples to confirm the effectiveness of the approaches we have developed.