In this paper, the stability problem is studied for inertial neural network with time-varying delays. The sampled-data control method is employed for the system design. First, by choosing a proper variable substitution, the original system is transformed into first-order differential equations. Then, an input delay approach is applied to deal with the stability of sampling system. Based on the Lyapunov function method, several sufficient conditions are derived to guarantee the global stability of the equilibrium. Furthermore, when employing an error-feedback control term to the slave neural network, parallel criteria regarding to the synchronization of the master neural network are also generated. Finally, some examples are given to illustrate the theoretical results.

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Stability of real time hybrid simulation (RTHS) has attracted considerable attention since actuator delay would deviate experiment results or even destabilize the real-time test. Previous studies have extensively investigated stability of RTHS for linear systems, while stability of RTHS for nonlinear system remains unclear. This study introduces the Takagi-Sugeno (T-S) method to describe the nonlinear behavior in a piecewise linear way, then investigates the stability of nonlinear system with time delay through the Lyapunov-Krasovskii (L-K) theory.Such approach successfully solves the stability problem of RTHS with coupled bilinear-hysteresis substructure and actuator delay, and proposes a stability criterion in the form of linear matrix inequality (LMI). It proves that the stability of RTHS is determined by the most unfavorable state of nonlinear system. In the SDOF case with stiffness softening, the initial elastic state is the most unfavorable; while for the MDOF case with multiple delays, the stability is determined by the overlap part of stable region of each nonlinear state. The computational simulation and experimental results show that the difference between linear-and nonlinear hysteretic system with time delay is that when instability occurs, latter could remain energy balanced since the time-delay energy is dissipated by hysteresis behavior, while energy accumulates in the former leading to unbounded responses. The proposed approach provides a potential tool for experimental design of RTHS before the test, the time-delay control during the test and error evaluation after the test.