Stability of real-time hybrid simulation (RTHS) has attracted considerable attention given that actuator delay might destabilize the real-time test, especially when the compensation is not sufficient. Previous research by the authors explored the stability of RTHS with time-varying delay, but the derived stability criteria are relatively conservative due to the application of the Lyapunov-Krasovskii (L-K) theory. For overcoming such defect and pursuing a more accurate stability analysis, this study introduces a delay decomposition approach to reduce the conservatism of matrix inequality with convexity property. For both constant- and time-varying delay systems, the delay decomposition approach performed remarkably in stability analysis. Moreover, with the increase in number of decomposition, this approach can further improve the accuracy of analysis results and reduce its conservatism; however, the computational efforts will rise rapidly. Computational simulation verified the effectiveness of the delay decomposition approach especially for the physical substructure involving a small stiffness ratio.

In a real time hybrid simulation (RTHS), the actuator delay might deviate experimental results, or even destabilize the real-time test. Currently, research is very limited on stability of multiple-degree-of-freedom (MDOF) structures with multiple delays. Using the Lyapunov-Krasovskii (L-K) method, this study proposes stability criteria for MDOF systems with multiple time-varying/constant delays, and derives a more accurate result. Application of criteria shows that the stability of time-varying delay system is smaller than the corresponding constant delay system. With number of DOF and delay increasing, the criterion accuracy decreases slowly for constant delay system; meanwhile, the stability difference between constant- and time-varying- delay system increases gradually. Such difference is significant with small stiffness ratio of physical substructure.

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.