H∞ control design for synchronisation of identical linear multi-agent systems

Abstract

In this paper we study the state synchronization problem of multi-agent systems subject to external additive perturbations. We consider high-order linear time-invariant multi-agent systems whose communication topology is encoded by an undirected and connected graph. We propose an H∞ control design technique based on a decentralized output feedback controller. We give sufficient conditions to ensure state synchronization with bounded L2 gain using a Lyapunov-based approach. These conditions are characterized in terms of matrix inequalities. Since these matrix inequality conditions are nonconvex and can not be solved straightforwardly, we propose a relaxation technique and an effective numerical procedure to design a suitable controller with guaranteed performance on the multi-agent distributed closed loop.

Synchronization in Networks of Identical Nonlinear Systems via Dynamic Dead Zones

“…, b n )T −1 ⊗ K). Consider now the Lyapunov function, independent of x 1 , defined as W (ε, σ) = V (ε) + ν1 n σ, with V defined as in (19) and ν > 0 a parameter to be defined. Following (21), we compute its time derivative aṡ…”

“…However, the definition of control architectures that allow mitigating the effect of these perturbations/phenomena over the networks is a topic widely open. Some authors have exploited H ∞ techniques in the case of networks of linear systems [18], [19], while in [20] the authors studied the problem of synchronization exploiting integral quadratic constraints (IQC). However, it is a well known fact that the extension of these techniques to the nonlinear framework presents several obstructions.…”