This paper introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without biases, we present a stability theorem that demonstrates the global exponential stability of linear systems under fully connected FFNN control. Utilizing principles from positive Lur'e systems and the positive Aizerman conjecture, our approach effectively addresses the challenge of ensuring stability in highly nonlinear systems. The crux of our method lies in maintaining sector bounds that preserve the positivity and Hurwitz property of the overall Lur'e system. We showcase the practical applicability of our methodology through its implementation in a linear system managed by a FFNN trained on output feedback controller data, highlighting its potential for enhancing stability in dynamic systems.

翻译：本文提出了一种用于分析带有一类全连接前馈神经网络控制器正反馈系统稳定性的新方法。通过为无偏置全连接FFNN建立扇区界，我们提出了一个稳定性定理，证明了线性系统在全连接FFNN控制下的全局指数稳定性。利用正Lur'e系统原理和正Aizerman猜想，我们的方法有效解决了高度非线性系统中确保稳定性的难题。该方法的核心在于保持扇区界，从而维持整个Lur'e系统的正性与Hurwitz特性。我们通过在由输出反馈控制器数据训练的FFNN管理的线性系统中实施该方法，展示了其实际应用价值，凸显了其在增强动态系统稳定性方面的潜力。