Monotone systems under positive feedback: multistability and a reduction theorem

For feedback loops involving single input, single output monotone systems with well-defined I/O characteristics, a recent paper by Angeli and Sontag provided an approach to determining the location and stability of steady states. A result on global convergence for multistable systems followed as a consequence of the technique. The present paper extends the approach to multiple inputs and outputs. A key idea is the introduction of a reduced system which preserves local stability properties.