Abstract
Relaxation oscillators typically consist of a hysteresis element and a dynamic feedback. The robustness of oscillations in such an interconnection is of interest in many applications. In particular, we seek the robustness margin on the component perturbations in the gap metric so that oscillatory behavior of the closed loop is preserved. A new distance measure for oscillatory signals utilizing time scaling is introduced for this purpose. The robustness of a system consisting of an ideal relay with hysteresis and an integrator has been studied in (Georgiou and Smith 2000). Here analogous results are derived for a system consisting of an integrator and a relay whose branches have non-zero slope. This system resembles the classical van der Pol oscillator more closely than the ideal relay system.
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