TY - GEN
T1 - Stability properties of infected networks with low curing rates
AU - Khanafer, Ali
AU - Başar, Tamer
AU - Gharesifard, Bahman
PY - 2014
Y1 - 2014
N2 - In this work, we analyze the stability properties of a recently proposed dynamical system that describes the evolution of the probability of infection in a network. We show that this model can be viewed as a concave game among the nodes. This characterization allows us to provide a simple condition, that can be checked in a distributed fashion, for stabilizing the origin. When the curing rates at the nodes are low, a residual infection stays within the network. Using properties of Hurwitz Mertzel matrices, we show that the residual epidemic state is locally exponentially stable. We also demonstrate that this state is globally asymptotically stable. Furthermore, we investigate the problem of stabilizing the network when the curing rates of a limited number of nodes can be controlled. In particular, we characterize the number of controllers required for a class of undirected graphs. Several simulations demonstrate our results.
AB - In this work, we analyze the stability properties of a recently proposed dynamical system that describes the evolution of the probability of infection in a network. We show that this model can be viewed as a concave game among the nodes. This characterization allows us to provide a simple condition, that can be checked in a distributed fashion, for stabilizing the origin. When the curing rates at the nodes are low, a residual infection stays within the network. Using properties of Hurwitz Mertzel matrices, we show that the residual epidemic state is locally exponentially stable. We also demonstrate that this state is globally asymptotically stable. Furthermore, we investigate the problem of stabilizing the network when the curing rates of a limited number of nodes can be controlled. In particular, we characterize the number of controllers required for a class of undirected graphs. Several simulations demonstrate our results.
KW - Constrained control
KW - Networked control systems
KW - Stability of nonlinear systems
UR - http://www.scopus.com/inward/record.url?scp=84905715736&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84905715736&partnerID=8YFLogxK
U2 - 10.1109/ACC.2014.6859418
DO - 10.1109/ACC.2014.6859418
M3 - Conference contribution
AN - SCOPUS:84905715736
SN - 9781479932726
T3 - Proceedings of the American Control Conference
SP - 3579
EP - 3584
BT - 2014 American Control Conference, ACC 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 American Control Conference, ACC 2014
Y2 - 4 June 2014 through 6 June 2014
ER -