A chain observer for a class of nonlinear systems with long multiple delays in output measurements

The main contribution of this paper is to present a chain observer for a class of nonlinear systems when the output measurements are affected by a long known and multiple bounded time-varying delay. The proposed observer is composed of a chain of observers with similar algorithm. Each observer estimates the state over a time horizon, while the first observer of the chain estimates the current state. The structure of each observer of the chain is based on the presence of a dynamical term which permits the compensation of the delay. The observer gains are computed by a set of parameterized Linear Matrix Inequalities (LMIs) which depends on the delay. A Lyapunov-Krasovskii functional is used to demonstrate the asymptotical convergence to zero of the observation error. The performance of the proposed observer is evaluated through a numerical example.