Immersion of nonlinear systems into linear systems modulo output injection

Abstract

Abstmcl-This paper deals with the problem of the immersion of a SISO sjstem into a linear up to an output injection one. For this class of sjstems Luenberger-like observes can be designed the djnamics of the error between the states of the obsener and the immersed controlled system is linear. Necessary and sufficient Conditions are firs1 stated within a r e v general framework. Efleetive computations and examples are then provided for uncontrolled and control-affine sjstems In particular the control-affine case is completel) (with a very slight restriction) sohed.

Homogeneous finite time observer for nonlinear systems with linearizable error dynamics

“…Usually, n = d but one can have n > d in the case of system immersion [2], [23]. Then, the observer design is quite simple since all nonlinearities are function of the output and known inputs.…”

“…The linearization by input-output injection, that consists in finding an equivalent observable linear system up to output injection, has been studied in [6], [14], [25], [26], [29], [42]. Extensions were given in [15], [38] using output dependent time scaling, and in [2], [23] using system immersion. Then, Luenberger based linear observer with asymptotically stable error dynamics can be designed.…”

Nonlinear observer for the PM synchronous motor

“…Besides, another interesting form, the so-called depending output observer normal form, was introduced by [30], and then was improved in [31] and [32]. The most recent normal form, called extended nonlinear observer normal form due to [33], allows us to enlarge the class of observer normal forms. It has been generalized by [34], [35], [36], [37], [38].…”

On emulated nonlinear reduced-order observers for networked control systems

“…To the best of our knowledge, it is the first time that reduced-order observers are built for NCS subject to scheduling. We start by considering a continuous-time observer design which comes from im-mersion and invariance techniques [9,3] and which allows one to recover many observer syntheses as mentioned in [9], such as linear Luenberger observers, highgain observers [10,5], observers for linear systems up to an output injection [11,7] and circle-criterion observers [2] to mention a few. A model is then derived for the observer design for NCS, which is based on a different set of coordinates compared to [16,17].…”