Monotone control systems

2003/10/01 by D. Angeli, David Angeli, E.D. Sontag +1 · 673 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Artificial intelligence #Computer science #Control (management) #Control system #Dynamical systems theory #Engineering #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical optimization #Mathematics #Monotone polygon #Monotonic function #Receptor Mechanisms and Signaling #Theoretical computer science

paper · doi:10.1109/tac.2003.817920

published in IEEE Transactions on Automatic Control 48(10), 1684-1698 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2003/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27

Abstract

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems.

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• Monotone Control Systems
• Monotone Systems with Inputs and Outputs
• Multi-Stability in Monotone Input/Output Systems
• Monotone and near-monotone network structure (part I)
• Monotone and near-monotone network structure (part II)