Add to ORKGFor a class of monotone operators T on the positive orthant of n-dimensional Euclidean space we introduce the concept of decay sets. These consist of points x satisfying T(x)<x. Considering the induced dynamical system x(k 1)=T(x(k)), we establish results relating stability properties of the origin, order conditions on T, and topological properties of decay sets. In particular, we construct paths in the decay sets and derive a quasi-invertibility result of the operator (Id-T).These results are applied to derive generalized small-gain type conditions for the input-to-state stability(ISS) of large-scale interconnections of (individually input-to-state stable) control systems: The interconnection topology together with the ISS gains yields a ...
The second edition of this textbook provides a single source for the analysis of system models repre...
Monotone systems in abstract Banach spaces have strong stability and convergence properties and have...
Monotone systems constitute one of the most important classes of dynamical systems used in mathemati...
For a class of monotone operators T on the positive orthant of n-dimensional Euclidean space we intr...
For a class of monotone operators T on the positive orthant of n-dimensional Euclidean space we intr...
For a class of monotone operators T on the positive orthant of n-dimensional Euclidean space we intr...
Summary. One of the key ideas in control theory is that of viewing a complex dynamical system as an ...
In this paper, we study positive invariance and attractivity properties for nonlinear control system...
In this paper, we study positive invariance and attractivity properties for nonlinear control system...
We develop a small-gain theory for systems described by set-valued maps between topological spaces. ...
International audienceThis survey article addresses the class of continuous-time systems where a sys...
International audienceThis survey article addresses the class of continuous-time systems where a sys...
International audienceThis survey article addresses the class of continuous-time systems where a sys...
International audienceThis survey article addresses the class of continuous-time systems where a sys...
In the stability analysis of large-scale interconnected systems it is frequently desirable to be abl...
The second edition of this textbook provides a single source for the analysis of system models repre...
Monotone systems in abstract Banach spaces have strong stability and convergence properties and have...
Monotone systems constitute one of the most important classes of dynamical systems used in mathemati...
For a class of monotone operators T on the positive orthant of n-dimensional Euclidean space we intr...
For a class of monotone operators T on the positive orthant of n-dimensional Euclidean space we intr...
For a class of monotone operators T on the positive orthant of n-dimensional Euclidean space we intr...
Summary. One of the key ideas in control theory is that of viewing a complex dynamical system as an ...
In this paper, we study positive invariance and attractivity properties for nonlinear control system...
In this paper, we study positive invariance and attractivity properties for nonlinear control system...
We develop a small-gain theory for systems described by set-valued maps between topological spaces. ...
International audienceThis survey article addresses the class of continuous-time systems where a sys...
International audienceThis survey article addresses the class of continuous-time systems where a sys...
International audienceThis survey article addresses the class of continuous-time systems where a sys...
International audienceThis survey article addresses the class of continuous-time systems where a sys...
In the stability analysis of large-scale interconnected systems it is frequently desirable to be abl...
The second edition of this textbook provides a single source for the analysis of system models repre...
Monotone systems in abstract Banach spaces have strong stability and convergence properties and have...
Monotone systems constitute one of the most important classes of dynamical systems used in mathemati...