Observer Design for Nonlinear Systems
Observer Design for Nonlinear Systems deals with the design of observers for the large
class of nonlinear continuous-time models. It contains a unified overview of a broad
range of general designs, including the most recent results and their proofs, such as the
homogeneous and nonlinear Luenberger design techniques.
The book starts from the observation that most observer designs consist in looking for
a reversible change of coordinates transforming the expression of the system dynamics
into some specific structures, called normal forms, for which an observer is known.
Therefore, the problem of observer design is broken down into three sub-problems:
• What are the available normal forms and their associated observers?
• Under which conditions can a system be transformed into one of these forms and
through which transformation?
• How can an inverse transformation that recovers an estimate in the given initial
coordinates be achieved?
This organisation allows the book to structure results within a united framework,
highlighting the importance of the choice of the observer coordinates for nonlinear
systems. In particular, the first part covers state-affine forms with their Luenberger
or Kalman designs, and triangular forms with their homogeneous high-gain designs.
The second part addresses the transformation into linear forms through linearization
by output injection or in the context of a nonlinear Luenberger design, and into
triangular forms under the well-known uniform and differential observability assumptions.
Finally, the third part presents some recently developed methods for avoiding the
numerically challenging inversion of the transformation. Observer Design for Nonlinear
Systems addresses students and researchers looking for an introduction to or an overview
of the state of the art in observer design for nonlinear continuous-time dynamical systems.
The book gathers the most important results focusing on a large and diffuse literature on
general observer designs with global convergence, and is a valuable source of information
for academics and practitioners.