2025/04/08 by Kang Tong, Tong, Kang, Christian Grußler +3
Computer Science · Engineering · #34A34 #34C12 #93C55 #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Neural Networks Stability and Synchronization #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2504.05941
openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the output has a single-peaked period. Under the assumption that the linear system is stable and has an impulse response that is strictly monotonically decreasing on its infinite support, we take a novel approach in using the framework of total positivity to address our main question. It is shown that unimodal self-oscillations can only exist if the number of positive and negative elements in a period coincides. Based on this result, we derive conditions for the existence of such oscillations, determine bounds on their periods, and address the question of uniqueness.