Proportional Control of Negative Feedback Physiological Systems

Understanding the dynamics of negative feedback physiological control systems is fundamental for assessing their stability and properties in healthy and diseased states. In this study, we aim to define a system-theoretic general mathematical framework to investigate the dynamics of physiological control systems that are supported by an external artificial controller with proportional action. A theorem is proposed to demonstrate the uniqueness and asymptotic stability of the equilibrium point. The proposed theorem is then implemented through a paradigmatic example of glucose-insulin regulation in type 1 Diabetes management, demonstrating its concrete applicability to a representative case of hybrid artificial-physiological controlled systems.