Dominant Mixed Feedback Design for Stable Oscillations

We present a design framework that combines positive and negative feedback for robust stable oscillations in closed loop. The design is initially based on graphical methods, to guide the selection of the overall strength of the feedback (gain) and of the relative proportion of positive and negative feedback (balance). The design is then generalized via linear matrix inequalities. The goal is to guarantee robust oscillations to bounded dynamic uncertainties and to extend the approach to passive interconnections. The results of this article provide a system-theoretic justification to several observations from system biology and neuroscience pointing at mixed feedback as a fundamental enabler for robust oscillations.