Synchronisation Results for an Interconnected Network of Nonlinear Systems with Diffusive Nonlinear Coupling using Contraction - Chauhan, Yashasvi; Sharma, B. B. (Journal of Applied Nonlinear Dynamics, 2026)
This paper presents a contraction theory based methodology for synchronisation of non-linearly coupled dynamical systems interconnected to constitute a complex network. Here, a systematic control procedure is presented to achieve synchronisation of complex network of proposed strict-feedback like class of nonlinear systems. The non-linear diffusive coupling function between different systems of the network is assumed to be in the form of bidirectional links. The proposed methodology can be applicable to any arbitrarily structure of linear/non-linear, bidirectional or unidirectional N-coupled systems in a network. Rigorous analytical results have been derived for coupled systems interacting through specific nonlinear coupling function which are interconnected in different networked topologies including Ring, Global, Star, Arbitrary etc. The analytical conditions for synchronisation are expressed in terms of bounds on coupling strength which are derived using partial contraction concepts blended with graph theory results. An example of complex networks is simulated to verify the theoretical results.