General framework in designing luenberger-like non-linear observer

The problem of designing Luenberger-like observer for non-linear Lipschitz systems is addressed. Based on using the coordinate transformation, the author classify many practical approaches of observer synthesis into direct and indirect methods. A generalised Lipschitz condition and the related stability condition are then employed to establish a general framework in designing the Luenberger-like observer dealing with both methods. Moreover, the proposed framework is interpreted in terms of some linear matrix inequalities (LMIs) which allows using numerical techniques to obtain a reduced order observer. Finally, some simulation examples are given to exhibit the effectiveness of the proposed observer synthesis approach.