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This study addresses the challenge of selecting sensors for linear time-varying (LTV) systems dynamically. We present a framework that designs an online sparse sensor schedule with performance guarantees using randomized algorithms for large-scale LTV systems. Our approach calculates each sensor’s contribution at each time in real-time and immediately decides whether to keep or discard the sensor in the schedule, with no possibility of reversal. Additionally, we provide new performance guarantees that approximate the fully-sensed LTV system with a multiplicative approximation factor and an additive one by using a constant average number of active sensors at each time. We demonstrate the validity of our findings through several numerical examples. 

This letter 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.