Nonlinear unknown input sliding mode observer based chaotic system synchronization and message recovery scheme with uncertainty

In the present manuscript, observer based synchronization and message recovery scheme is discussed for a system with uncertainties. LMI conditions are analytically derived solution of which gives the observer design matrices. Earlier approaches have used adaptive laws to address the uncertainties, however in present work, decoupling approach is used to make observer robust against uncertainties. The methodology requires upper bounds on nonlinearity and the message signal and estimates for these bounds are generated adaptively. Thus no information about the nature of nonlinearity and associated Lipschitz constant is needed in proposed approach. Message signal is recovered using equivalent output injection which is a low pass filtered equivalent of the discontinuous effort required to maintain the sliding motion. Finally, the efficacy of proposed Nonlinear Unknown Input Sliding Mode Observer (NUISMO) for chaotic communication is verified by conducting simulation studies on two chaotic systems i.e. third order Chua circuit and Rossler system.