infinite networks
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2021 ◽  
Vol 43 ◽  
pp. 101097
Author(s):  
Siyuan Liu ◽  
Navid Noroozi ◽  
Majid Zamani


Author(s):  
Andrii Mironchenko ◽  
Christoph Kawan ◽  
Jochen Glück

AbstractWe consider infinite heterogeneous networks, consisting of input-to-state stable subsystems of possibly infinite dimension. We show that the network is input-to-state stable, provided that the gain operator satisfies a certain small-gain condition. We show that for finite networks of nonlinear systems this condition is equivalent to the so-called strong small-gain condition of the gain operator (and thus our results extend available results for finite networks), and for infinite networks with a linear gain operator they correspond to the condition that the spectral radius of the gain operator is less than one. We provide efficient criteria for input-to-state stability of infinite networks with linear gains, governed by linear and homogeneous gain operators, respectively.



Author(s):  
Andrii Mironchenko

Abstract We introduce the concept of non-uniform input-to-state stability for networks. It combines the uniform global stability with the uniform attractivity of any subnetwork while it allows for non-uniform convergence of all components. For an infinite network consisting of input-to-state stable subsystems, which do not necessarily have a uniform $\mathscr{K}\mathscr{L}$-bound on the transient behaviour, we show the following: if the gain operator satisfies the uniform small-gain condition, then the whole network is non-uniformly input-to-state stable and all its finite subnetworks are input-to-state stable.





2021 ◽  
Vol 54 (9) ◽  
pp. 72-77
Author(s):  
Navid Noroozi ◽  
Andrii Mironchenko ◽  
Christoph Kawan ◽  
Majid Zamani
Keyword(s):  


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Christian Budde ◽  
Marjeta Kramar Fijavž
Keyword(s):  




Author(s):  
Maryam Sharifi ◽  
Abdalla Swikir ◽  
Navid Noroozi ◽  
Majid Zamani


2020 ◽  
Vol 52 (2) ◽  
pp. 463-490
Author(s):  
Seva Shneer ◽  
Alexander Stolyar

AbstractWe study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For finite networks we establish stability and some steady-state moment bounds under natural conditions and rather weak assumptions on utility functions. These results are obtained using direct applications of Lyapunov–Foster-type criteria, and apply to a wide class of systems, including those for which fluid-limit-based approaches are not applicable. We then establish stability and some steady-state moment bounds for two classes of infinite networks, with single-hop and multi-hop message routes. These results are proved by considering the infinite systems as limits of their truncated finite versions. The uniform moment bounds for the finite networks play a key role in these limit transitions.



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