TY - JOUR
T1 - A bounded complementary sensitivity function ensures topology-independent stability of homogeneous dynamical networks
AU - Blanchini, Franco
AU - Casagrande, Daniele
AU - Giordano, Giulia
AU - Viaro, Umberto
PY - 2018
Y1 - 2018
N2 - This paper investigates the topology-independent stability of homogeneous dynamical networks, composed of interconnected equal systems. Precisely, dynamical systems with identical nominal transfer function F(s) are associated with the nodes of a directed graph, whose arcs account for their dynamic interactions, described by a common nominal transfer function G(s). It is shown that topology-independent stability is guaranteed for all possible interconnections with interaction degree (defined as the maximum number of arcs leaving a node) equal at most to N if the ∞-norm of the complementary sensitivity function NF(s)G(s)[1+NF(s)G(s)]-1 is less than 1. This bound is nonconservative in that there exist graphs with interaction degree N that are unstable for an ∞-norm greater than 1. When nodes and arcs transferences are affected by uncertainties with norm bound K> 0, topology-independent stability is robustly ensured if the ∞-norm is less than 1/(1+2NK). For symmetric systems, stability is guaranteed for all topologies with interaction degree at most N if the Nyquist plot of NF(s)G(s) does not intersect the real axis to the left of-1/2. The proposed results are applied to fluid networks and platoon formation.
AB - This paper investigates the topology-independent stability of homogeneous dynamical networks, composed of interconnected equal systems. Precisely, dynamical systems with identical nominal transfer function F(s) are associated with the nodes of a directed graph, whose arcs account for their dynamic interactions, described by a common nominal transfer function G(s). It is shown that topology-independent stability is guaranteed for all possible interconnections with interaction degree (defined as the maximum number of arcs leaving a node) equal at most to N if the ∞-norm of the complementary sensitivity function NF(s)G(s)[1+NF(s)G(s)]-1 is less than 1. This bound is nonconservative in that there exist graphs with interaction degree N that are unstable for an ∞-norm greater than 1. When nodes and arcs transferences are affected by uncertainties with norm bound K> 0, topology-independent stability is robustly ensured if the ∞-norm is less than 1/(1+2NK). For symmetric systems, stability is guaranteed for all topologies with interaction degree at most N if the Nyquist plot of NF(s)G(s) does not intersect the real axis to the left of-1/2. The proposed results are applied to fluid networks and platoon formation.
UR - http://resolver.tudelft.nl/uuid:rbab01887-339c-47d2-8550-4ebd8ce8d1d1
UR - http://www.scopus.com/inward/record.url?scp=85029002008&partnerID=8YFLogxK
U2 - 10.1109/TAC.2017.2737818
DO - 10.1109/TAC.2017.2737818
M3 - Article
AN - SCOPUS:85029002008
SN - 0018-9286
VL - 63
SP - 1140
EP - 1146
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 4
ER -