In this paper the problem of hyperbolic observer design for a class of nonlinear systems is addressed for the first time. The asymptotic stability of the estimation error dynamics is proven by employing the Lyapunov stability analysis method and using Taylor series for hyperbolic functions, and then the sufficient conditions are derived in the form of Linear Matrix Inequalities (LMIs). Also a hyperbolic non-fragile adaptive observer is introduced for a class of uncertain nonlinear systems with time delay. It is shown that the proposed observer performs effectively in dealing with large estimation errors. Three illustrative examples of Chen, Rössler and a financial system are provided which corroborate the effectiveness of the propose method.
