Gain-scheduled synchronization of parameter varying systems via relative H∞ consensus with application to synchronization of uncertain bilinear systems

The problem of synchronization of complex dynamical networks of interconnected systems has received much attention recently in the context of multi-agent consensus. This work extends our previous research on H∞ consensus-based synchronization to systems which require a time-varying reference for synchronization. Time variations of systems coefficients pose an additional difficulty in addressing system robustness, since many standard robust control and filtering techniques developed for time-invariant systems are not directly transferable to time-varying systems. While in some situations the issue can be circumvented by restricting attention to a finite-horizon version of the problem, such an approach may not be suitable in synchronization problems. For instance, synchronization of nonlinear systems exhibiting chaotic behaviour requires the system to be continuously ‘locked’ into synchronous operation, otherwise even small discrepancies between trajectories will cause the system to lose synchrony in a very short time. In this work we propose a protocol for interconnecting parameter--varying systems which guarantees a specified level of H∞ transient consensus between the agents. The algorithm uses a consensus-preserving interpolation and produces continuous (in the scheduling parameter) coefficients for the protocol. An application to synchronization of uncertain bilinear systems is discussed.  This research has been supported by the Australian Research Council under Discovery Projects funding scheme. The results of this work have been published in [V. Ugrinovskii, Gain-scheduled synchronization of parameter varying systems via relative H∞ consensus with application to synchronization of uncertain bilinear systems, Automatica, 50(11), 2880-2887, 2014.]