Synchronization in Multi-scroll systems on strongly connected networks
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Abstract: In this work, we study the synchronization problem in complex dynamic networks of Piece Wise Linear (PWL) systems. PWL systems exhibit multi-scrolls and belong to a special class of Unstable Dissipative Systems (UDS). We consider strongly connected directed networks and linear diffusive couplings. The synchronization regions are computed using the concept of disagreement vectoars, generalized algebraic connectivity of the network topology, and Lyapunov functions, which provide lower bounds for the network’s coupling gain. Then, different combinations of linear diffusive coupling are explored by changing the observed and measured variables to illustrate the contribution of our results. The theoretical results are validated by numerical simulations.