Nonlinear observer design using Lyapunov's auxiliary theorem

An asymptotic observer for batch processes with single biogas measurement

“…Let us point out a few (e.g. Gauthier & Kupka [1998] Kazantzis & Kravaris [1998], Krener & Isidori [1983]) as well as the interesting and nicely survey paper by Krener (Krener [2004]). In the present paper, we would like to address a state observation issue that, as far as we know, has yet been addressed, i.e.…”

Immersion and invariance observers with time-delayed output measurements

“…Again, these results consist in finding a transformation that linearizes part of the plant and then applying standard linear or hight gain observer design techniques. In [10], the ideas of their previous work [5] are extended to the case when the output measurements are subject to constant time-delays. The authors propose a nonlinear observer with state-dependent gain which is computed from the solution of a system of first-order singular PDEs.…”

“…We refer the reader to [4] and references therein for a fairly complete literature review of the existing observer design techniques for nonlinear systems. More recently, in [5] and [6], the early ideas of Luenberger are extended to the nonlinear case. In these papers, sufficient conditions for the existence of linear observers with nonlinear output injection terms are derived in terms of the solution of a partial differential equation (PDE).…”

Observabilty singularities and observer design: dual immersion approach

“…On the other hand, owing to the fact that it is easier to design an observer for linear systems, the natural approach to designing nonlinear observers, adopted by several researchers [15,25,22,14,12,1,2], consist in transforming the original system into i) either a linear one plus a nonlinear part having some special structures ii) or a linear one plus a nonlinear part depending only on the input and the output so the observer has linear error dynamics.…”