The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient -but to some extent, also necessary -to ensure synchronization with the diffusive static output coupling often considered in the literature. synchronization to a common value. The convergence of such consensus algorithms has attracted much attention in the recent years. It only requires a weak form of connectivity for the communication graph [1,2,3,4,5].In the synchronization literature, the emphasis is on the individual dynamics rather than on the communication limitations: the communication graph is often assumed to be complete (or all-to-all), but in the absence of communication, the time-evolution of the systems' variables can be oscillatory or even chaotic. The system dynamics can be modified through the information exchange, and, as in the consensus problem, the goal of the interconnection is to reach synchronization to a common solution of the individual dynamics [6,7,8,9].Coordination problems encountered in the engineering world can often be rephrased as consensus or synchronization problems in which both the individual dynamics and the limited communication aspects play an important role. Designing interconnection control laws that can ensure synchronization of relevant variables is therefore a control problem that has attracted quite some attention in the recent years [10,11,12,13,14].The present paper deals with a fairly general solution of the synchronization problem in the linear case. Assuming N identical individual agents dynamics each described by the linear state-space model (A, B, C), the main result is the construction of a dynamic output feedback controller that ensures exponential synchronization to a solution of the linear systemẋ = Ax under the following assumptions: (i) A has no exponentially unstable mode, (ii) (A, B) is stabilizable and (A, C) is detectable, and (iii) the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms, studied recently, corresponding to the particular case A = 0 [1,2]. The generalization includes the non-trivial examples of synchronizing harmonic oscillators or chains of integrators.The proposed dynamic controller structure proposed in this paper differs from the static diffusive coupling often considered in the synchronization literature, which requires more stringent assumptions on the communication graph. For instance, the results in the recent paper [15] assume a time-invariant topology. The paper also provides sufficient conditions for synchronization by static diffusive couplin...

Abstract-In this paper we study robustness of consensus in networks of coupled single integrators driven by white noise. Robustness is quantified as the H2 norm of the closed-loop system. In particular we investigate how robustness depends on the properties of the underlying (directed) communication graph. To this end several classes of directed and undirected communication topologies are analyzed and compared. The trade-off between speed of convergence and robustness to noise is also investigated.

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient -but to some extent, also necessary -to ensure synchronization with the diffusive static output coupling often considered in the literature.

In this paper, we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. The global convergence analysis on the N -torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space.

This paper provides synchronization conditions for networks of nonlinear systems. The components of the network (referred to as "compartments" in this paper) are made up of an identical interconnection of subsystems, each represented as an operator in an extended L 2 space and referred to as a "species". The compartments are, in turn, coupled through a diffusion-like term among the respective species. The synchronization conditions are provided by combining the input-output properties of the subsystems with information about the structure of network. The paper also explores results for state-space models, as well as biochemical applications. The work is motivated by cellular networks where signaling occurs both internally, through interactions of species, and externally, through intercellular signaling. The theory is illustrated providing synchronization conditions for networks of Goodwin oscillators.