Nonlinear signal-based control (NSBC) has recently been developed for nonlinear structural systems. NSBC shows high tracking performance in structural systems that display parameter variations during control practice. This control approach is also efficient for substructuring experimentation, an advanced technique based on real-time interaction between physical experiments and numerical simulations. NSBC allows controller design to be based on classical control theory, with the controllers expressed by transfer functions. Without losing this benefit, this study proposes to analyse the stability of NSBC for nonlinear structural systems and a pure time delay by employing the Nyquist stability criterion, which is also classified into classical stability theory. Then stability analysis that regards the nonlinearity as a parameter variation associated with the linear model of the controlled system has been established in this study. The efficiency and practicality of the stability analysis are examined via numerical control practices for various nonlinear single- and multiple-degree-of-freedom (S/MDOF) systems having pure time delay. In the examination, the controlled systems are nonlinear SDOF and 2DOF systems with different types of nonlinear springs. In the numerical simulations, two control practices for NSBC (i.e., the nonlinear signal feedback action with or without the error feedback action) have offered excellent control with near 100% accuracy. Stability analysis of NSBC has accurately provided the stability conditions for the nonlinear controlled systems with a pure time delay.
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