<p>With the rapid development of artificial intelligence algorithms, the integration of intelligent methods with active disturbance rejection control (ADRC) has emerged as a significant trend in control engineering. However, rigorous stability analysis for such integration remains lacking, and even for ADRC employing time-varying gains, comprehensive stability frameworks have yet to be established. This paper addresses general linear ADRC with time-varying gains and derives two explicit conditions that guarantee closed-loop stability. Based on the derived conditions, a quantitative protective design method is proposed to ensure system stability during gain adaptation. Furthermore, the conditions are proven effective for systems with nonlinear internal uncertainties. This theoretical foundation provides rigorous support for practical ADRC applications employing time-varying and adaptive gains. Comparative simulations validate both the necessity of the proposed conditions and the effectiveness of the protective design method.</p>