A Unified LMI‐Based Observer Design Framework for Nonlinear Differential Algebraic Equations

ABSTRACT This work provides a novel nonlinear observer design for a class of nonlinear systems modeled as differential algebraic equations. Usual notions such as inputs, outputs, measurement noise, process noise, and external disturbances are embedded in those of measurable and unmeasurable signals, which is, in principle, the only relevant distinction from the observer point of view. The result of such change of perspective is a uniform methodology whose advantages are: (i) Providing a unified framework which comprises former proposals as particular cases; (ii) enabling a variety of modeling options that naturally incorporate constraints; (iii) allowing design conditions in the form of a finite set of matrix inequalities resulting in observer gains that depend nonlinearly on estimated states, (iv) incorporation of reduced‐order observers as a particular case. Detailed examples are included to give an account of the proposal performance against former methodologies, which, as proven, are less general (asking for special structures of the nonlinear model) or compromise numerical efficiency (due to the presence of bilinear matrix inequalities).