Stability Analysis of Real-Time Hybrid Simulation with Time-Varying Delay through a Delay Decomposition Approach

Abstract

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.