State synchronization of perturbed nonlinear switching systems via robust interval state observers

In this paper, a switched interval state observer-based synchronization method is developed. Such an observer is applied to reconstruct the state of perturbed nonlinear switched systems exhibiting chaotic behavior and subject to unknown but bounded exogenous perturbations and uncertainties. The stability study with Lyapunov approach is formulated in the form of linear matrix inequalities (LMIs) to calculate the observation gain matrix. Simulation results are provided to highlight the chaotic aspect of the studied systems and to reconstruct the lower and upper bounds of the unavailable state variables. Furthermore, a transmitted signal is synchronized with a restituted one, via nonlinear perturbed switched systems and nonlinear robust switched interval observer, to prove the high performance of the elaborated transmission strategy.