TY - JOUR
T1 - Convergence in uncertain linear systems
AU - Fabiani, Filippo
AU - Belgioioso, Giuseppe
AU - Blanchini, Franco
AU - Colaneri, Patrizio
AU - Grammatico, Sergio
PY - 2020
Y1 - 2020
N2 - State convergence is essential in many scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, computational game theory, multi-agent learning over networks. In this paper, we study for the first time the state convergence problem in uncertain linear systems. Preliminarily, we characterize state convergence in linear systems via equivalent linear matrix inequalities. In the presence of uncertainty, we complement the canonical definition of (weak) convergence with a stronger notion of convergence, which requires the existence of a common kernel among the generator matrices of the difference/differential inclusion (strong convergence). We investigate under which conditions the two definitions are equivalent. Then, we characterize strong and weak convergence via Lyapunov arguments, (linear) matrix inequalities and separability of the eigenvalues of the generator matrices. Finally, we show that, unlike asymptotic stability, state convergence lacks of duality.
AB - State convergence is essential in many scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, computational game theory, multi-agent learning over networks. In this paper, we study for the first time the state convergence problem in uncertain linear systems. Preliminarily, we characterize state convergence in linear systems via equivalent linear matrix inequalities. In the presence of uncertainty, we complement the canonical definition of (weak) convergence with a stronger notion of convergence, which requires the existence of a common kernel among the generator matrices of the difference/differential inclusion (strong convergence). We investigate under which conditions the two definitions are equivalent. Then, we characterize strong and weak convergence via Lyapunov arguments, (linear) matrix inequalities and separability of the eigenvalues of the generator matrices. Finally, we show that, unlike asymptotic stability, state convergence lacks of duality.
UR - http://www.scopus.com/inward/record.url?scp=85085936651&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2020.109058
DO - 10.1016/j.automatica.2020.109058
M3 - Article
AN - SCOPUS:85085936651
SN - 0005-1098
VL - 119
JO - Automatica
JF - Automatica
M1 - 109058
ER -