A tunable mixed feedback oscillator

TL;DR

This paper analyzes how mixed positive and negative feedback loops can produce robust, tunable oscillations in systems, using a three-dimensional Lure model and extending to larger and uncertain systems.

Contribution

It provides a system-theoretic analysis of mixed feedback mechanisms for oscillation control, extending to larger and uncertain systems.

Findings

Mixed feedback enables robust oscillations.

Dominance theory confirms feedback as a fundamental enabler.

Results extend to larger and uncertain systems.

Abstract

The interplay of positive and negative feedback loops on different time scales appears to be a fundamental mechanisms for robust and tunable oscillations in both biological systems and electro-mechanical systems. We develop a detailed analysis of a basic three dimensional Lure model to show how controlled oscillations arise from the tuning of positive and negative feedback strengths. Our analysis is based on dominance theory and confirms, from a system-theoretic perspective, that the mixed feedback is a fundamental enabler of robust oscillations. Our results are not limited to three dimensional systems and extend to larger systems via passivity theory, and to uncertain systems via small gain arguments.