Controlling nonlinear systems in the presence of matched/mismatched and vanishing/non-vanishing perturbations remains one of the key challenges since these factors often lead to instability and degraded performance. The H-infinity sliding mode control ( \({H}_\infty \) SMC) has recently gained attention for addressing such issues. However, most existing methods still struggle with unmatched non-vanishing perturbations of unknown bounds and often produce conservative results due to trade-offs between performance and robustness. In this paper, an adaptive integral dynamic \({H}_\infty \) SMC approach is proposed for nonlinear strict-feedback systems subject to fluctuating perturbations. The proposed design is built upon two components: (i) an adaptive integral quasi-SMC to compensate matched perturbations without requiring upper bounds, eliminate reaching phase, avoid chattering, and prevent amplification in unmatched perturbations; and (ii) an integral dynamic \({H}_\infty \) control law to handle the remaining matched dynamics and mismatched perturbations. The latter is synthesized using energy dissipation and Lyapunov analysis based on an \({H}_\infty \) algebraic Riccati equation (HARE) and further optimized through Gaussian quantum particle swarm optimization (GQPSO) to reduce conservatism and ensure robust global solutions. Simulation results verify that the proposed controller achieves robust stability and performance with bounded closed-loop signals, reduced computational demand, and adequate control effort, demonstrating superior performance compared to existing methods.
