Section: New Results

Observability and observer design for nonlinear systems

Observability analysis and observer design are important issues in the field of control theory. Some recent results are listed below:

• An epistemology of observation theory and its application in the design of software sensor in power electronics have been presented in [42] .

• New results on observability and detectability of singular linear systems with unknown inputs have been developed in [12] .

• The paper [47] supplies a new algorithm to compute the internal dynamics (or inversion dynamics) of affine MIMO control nonlinear systems.

• The design of observers for nonlinear systems with unknown, time-varying, bounded delays, on both state and input, still constitutes an open problem. In [28] , we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a Lyapunov-Krasovskii functional. Sufficient conditions have been provided to prove the practical stability of the observer.

• An influence of restricted isometry property to the observability under sparse measurements has been analyzed in [65] .

• The paper [38] , [79] concerns the design of a nonlinear observer through a transformation of a nonlinear system into an observer form that supports a high gain observer. Sufficient geometrical condition has been deduced to guarantee the existence of change of coordinates allowing the transformation of a nonlinear system into the proposed normal form. In [80] , the Partial Observability Normal Forms (PONF) of nonlinear dynamical systems have been investigated. Necessary and sufficient conditions for the existence of a diffeomorphism bringing the original nonlinear system into a PONF have been established.