Efficient finite abstraction of mixed monotone systems
We present an efficient computational procedure for finite abstraction of discrete-time mixed
monotone systems by considering a rectangular partition of the state space. Mixed …
monotone systems by considering a rectangular partition of the state space. Mixed …
Tight decomposition functions for continuous-time mixed-monotone systems with disturbances
The vector field of a mixed-monotone system is decomposable via a decomposition function
into increasing (cooperative) and decreasing (competitive) components, and this …
into increasing (cooperative) and decreasing (competitive) components, and this …
Traffic network control from temporal logic specifications
We propose a framework for generating a signal control policy for a traffic network of
signalized intersections to accomplish control objectives expressible using linear temporal …
signalized intersections to accomplish control objectives expressible using linear temporal …
Stability of traffic flow networks with a polytree topology
We consider global stability of a flow network model for vehicular traffic. Standard
approaches which rely on monotonicity of flow networks for stability analysis do not …
approaches which rely on monotonicity of flow networks for stability analysis do not …
Rational systems in the plane
Full article: Rational systems in the planeEdited by Gerry LadasIn this section, we present some
open problems and conjectures about some interesting types of difference equations. Please …
open problems and conjectures about some interesting types of difference equations. Please …
Global stability for mixed monotone systems
HL Smith - Journal of Difference Equations and Applications, 2008 - Taylor & Francis
We show that the embedding method described in J.-L. Gouzé and P. Hadeler (Monotone
flows and order intervals, Nonlinear World 1 (1994), pp. 23–34) and HL Smith (The discrete …
flows and order intervals, Nonlinear World 1 (1994), pp. 23–34) and HL Smith (The discrete …
Global asymptotic stability for discrete single species population models
We present some basic discrete models in populations dynamics of single species with
several age classes. Starting with the basic Beverton‐Holt model that describes the change …
several age classes. Starting with the basic Beverton‐Holt model that describes the change …
Tight remainder-form decomposition functions with applications to constrained reachability and guaranteed state estimation
In this article, we propose a tractable family of remainder-form mixed-monotone
decomposition functions that are useful for overapproximating the image set of nonlinear …
decomposition functions that are useful for overapproximating the image set of nonlinear …
Boundedness of solutions and stability of certain second-order difference equation with quadratic term
We consider the second-order rational difference equation xn+ 1= γ+ δ xnxn− 1 2, x_ n+ 1=
γ+ δ x_ nx^ 2 _ n-1, where γ, δ are positive real numbers and the initial conditions x− 1 x_-1 …
γ+ δ x_ nx^ 2 _ n-1, where γ, δ are positive real numbers and the initial conditions x− 1 x_-1 …