A chain observer for nonlinear long constant delay systems: A matrix inequality approach

This paper proposes a new state observer for nonlinear systems with non negligible and different time delays in the state, output and input and Lipschitz nonlinearity. The proposed observer is composed of a chain of observers with similar algorithm. Each of them estimates the states in different time instants, while the last observer estimates the state in the present time. Conditions for stability of the observer are translated into linear matrix inequalities (LMIs) which facilitates the design of observer gains. Simulation results demonstrate effectiveness of this observer.