In this letter, we propose a new observer error linearization approach that is called reduced-order dynamic observer error linearization (RDOEL), which is a modified version of dynamic observer error linearization (DOEL). We introduce the concepts and properties of RDOEL, and provide a complete solution to RDOEL with one integrator. Moreover, we show that it is also a complete solution to a simple case of DOEL.

In this letter, an illustrative example is given, which shows that the number of integrators needed for the dynamic observer error linearization using integrators can not be bounded by a function of the dimension of the system and the number of outputs in contrast to dynamic feedback linearization results.

In this paper we consider an approximation method of a formal linearization which transform time-varying nonlinear systems into time-varying linear ones and its applications. This linearization is a kind of a coordinate transformation by introducing a linearizing function which consists of the Chebyshev polynomials. The nonlinear time-varying systems are approximately transformed into linear time-varying systems with respect to this linearizing functions using Chebyshev expansion to the state variable and Laguerre expansion to the time variable. As applications, nonlinear observer and filter are synthesized for time-varying nonlinear systems. Numerical experiments are included to demonstrate the validity of the linearization. The results show that the accuracy of the approximation by the linearization improves as the order of the Chebyshev and Laguerre polynomials increases.

There exists a class of nonlinear systems which fail to have a well-defined relative degree but have a robust relative degree. We have removed the full relative degree assumption which the previous results required, and have provided a local state observer for nonlinear systems that have robust relative degree γ n and have detectability property in some sense. The proposed observer utilizes the coordinate change which transforms the system into an approximate normal form. Using the proposed method, we constructed an observer for the ball and beam system on a vibrating frame. Simulation results reveal that substantial improvement in the performance is achieved compared with other local observers.