<p>In an aging society, exoskeleton research is of great importance for improving mobility and balance in the elderly facing physical function decline. This study investigates the impact of time delay on the stability of a hip-exoskeleton-assisted human gait model. First, the governing equation of a 3-link human walking model controlled by hybrid zero dynamics is derived. Then, stability analysis is carried out using an error function represented by a second-order delay differential equation. Stability charts for the exoskeleton control gains are obtained using the D-decomposition method for different delays, showing that time delays deteriorate system stability. Furthermore, simulations identify four distinct gait patterns (fall state, fail state, unstable state and stable state) correlated with the stability charts, demonstrating that the theoretical stability results based on the error function serve as a necessary condition for the stable gait. Mechanical energy consumption analysis suggests that near stability boundaries, the exoskeleton may hinder movement, which indicates insufficient robustness in the presence of perturbations. This study underscores the importance of addressing time delays in the design of effective exoskeleton systems.</p>