Robust-observer design for nonlinear systems with delayed measurements using time-averaged Lyapunov stability criterion

This paper developed an observer design for a matrix-Lipchitz nonlinear system with measurement delay that can achieve a desired $ {\mathcal{L}}_{2} $ performance in the presence of modeling uncertainties, input disturbance, and measurement noise. The observer was shown to be stable in the absence of disturbances and modeling uncertainties. The equations for the observer design were shown to be both necessary and sufficient. Furthermore, the observer design was formulated as linear matrix inequality (LMI) that can be solved offline using commercial solvers. Compared to previous literature, the proposed observer does not require the underlying system to be stable. The observer design procedure is demonstrated through two illustrative examples.