Observer design for a class of nonlinear systems with long delay in output measurements: an LMI approach

This paper proposes a new state observer for a class of nonlinear systems with non negligible time delays in the output and Lipschitz nonlinearity. The proposed observer is composed of a chain of observers each of which estimates the states in different time instants, while the last observer estimates the state in the present time. This observer,unlike the previously introduced chain-like observers, introduces similar structure for all of the observation algorithms, is applicable for both of the stable and unstable nonlinear systems and has no limit for the value of time delay. Conditions for stability of the observer are translated into linear matrix inequalities (LMIs) to obtain the observer gains. Simulation results demonstrate effectiveness of this observer for both of the stable and unstable systems.