this paper studies output FEEDBACK control of pure-FEEDBACK systems with immeasurable states and completely non-affine property. Since availability of all the states is usually impossible in the actual process, we assume that just the system output is measurable and the system states are not available. First, to estimate the immeasurable states a state observer is designed. Relatively fewer results have been proposed for pure FEEDBACK systems because the cascade and non-affine properties of pure-FEEDBACK systems make it difficult to find the explicit virtual controls and actual control. Therefore, by employing the singular perturbation theory in back-stepping control procedure, the virtual/actual control inputs are derived from the solutions of a series of fast dynamical equations which can avoid the “explosion of complexity’’ inherently existing in the conventional back-stepping design. The stability of the resulting closed-loop system is proved by Tikhonov’s theorem in the singular perturbation theory. Finally, the detailed simulation results are provided to demonstrate the effectiveness of the proposed controller, which can overcome the non-affine property of pure-FEEDBACK systems with lower complexity and fewer design parameters.

This study examines the comparative effectiveness of automated FEEDBACK from AI-driven language assessment tools and traditional human FEEDBACK in improving language learning outcomes. As artificial intelligence (AI) becomes increasingly integrated into educational technology, understanding its role in supporting language learners is critical. To address this, we conducted a 12-week controlled experiment with 80 EFL (English as a Foreign Language) learners, dividing participants into two groups: one receiving FEEDBACK from an AI-driven tool and the other from human instructors. Language proficiency improvements were assessed in grammar, vocabulary, and pronunciation. Findings reveal that both FEEDBACK methods significantly enhanced language skills. Human FEEDBACK proved superior in fostering gains in pronunciation and contextual understanding, while AI-driven FEEDBACK excelled in detecting and correcting grammatical errors. These results suggest that a hybrid model, blending AI and human FEEDBACK, could provide the most effective support for language learners. This research enriches the literature on AI in education and offers practical insights for incorporating AI tools into language learning curricula.