Monotone control systems

By David Angeli, Eduardo Sontag. IEEE Transactions on Automatic Control, 2002

723 citations recorded by the source corpus.

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.

Subfields: Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/1310961ea4a9b6d1d45a0d273c4c6fd4d24e1f8e

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Citations in the corpus

A Differential Lyapunov Framework for Contraction Analysis (2012, background): “Equation (49) is also a time-varying monotone system [5], [47], and its stability properties have been studied by many authors [30], [53].”
Global attractivity, I/O monotone small-gain theorems, and biological delay systems (2005, neutral): “See for instance Ji Fa [16], and de Leenheer, Angeli and Sontag [22].”
Monotone Chemical Reaction Networks (2007, background): “Monotone dynamical systems have recently been extended to monotone input-output systems in [ 2 ] in order to facilitate the study of interconnections of such systems (cascades, feedback).”
Distributed control of positive systems (2011, methodology): “m 5 with Theorem 3 gives a linear programming formulation of the problem to minimize input-output gain: August 10, 2018 DRAFT 10 Corollary 7: Let D be the set of m×m diagonal matrices with entries in [0,1]. Suppose that D is scalar and that A+ELF is Metzler for all L ∈ D. If the matrices B,C,D and F”
Set Propagation Techniques for Reachability Analysis (2021, neutral): “Deﬁnition 12 (Monotone dynamics; see [94, Def.”
Online Verification of Automated Road Vehicles Using Reachability Analysis (2014, methodology): “1 (Monotone dynamics; see [57]): A system is monotone with respect to the initial state x(0) ∈ R(0) and inputs u(t) ∈ U when the following property holds for the solution χ(t, x(0), u(·)):”
Nonmonotone systems decomposable into monotone systems with negative feedback (2006, background): “In [1], Angeli and Sontag construct a theory of monotone control systems of the form x = f (x, u) (1) y = h(x) where the state space is partially ordered, the function space of controls u = u(t) is partially ordered, and the output space is partially ordered.”