Chain observer for Lipschitz non-linear systems with long time-varying delayed measurements

The main contribution of this study is to present a chain observer for Lipschitz non-linear systems when the output measurements are affected by a long known and bounded time-varying delay. The proposed chain observer is composed by a set of observers with similar algorithms. Each observer estimates the state in 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 time-varying delay. The observer gain is computed by solving parameterised linear matrix inequalities (LMIs) which depend on the delay. The less conservative Lipschitz condition allows to manage less restrictive LMI stability conditions, which leads to a more general class of Lipschitz non-linear systems. A Lyapunov-Krasovskii functional is used to demonstrate that the estimation error converges asymptotically to zero. The performance of the proposed observer is evaluated through numerical examples. The observer exhibits good estimation of the system state, even in the presence of significant delayed measurements.