A nonlinear updated gain observer for MIMO systems: Design, analysis and application to marine surface vessels

In this paper, the state estimation problem of a class of multi-input-multi-output nonlinear systems with measurement noise is studied. We develop an extended updated-gain high gain observer to make a tradeoff between reconstruction speed and measurement noise attenuation. The designed observer, whose gains are driven by nonlinear functions of the available output estimation errors, has the ability to reconstruct system states quickly and reduce the effect of measurement noise. We establish that, if there exists a state feedback law exponentially stabilizing the system with respect to an invariant set, the estimations and estimation errors are bounded. Besides, the trajectories of state- and output-feedback (based on the proposed observer) are sufficiently close, namely performance recovery. The observer performance is illustrated by various examples in marine control, including a case of transformation into the predefined structure.