Nonlinear observers for locally uniformly observable systems (original) (raw)

Local observer design for nonlinear systems

Mathematical and Computer Modelling, 2002

This paper is a geometric study of the local observer design for nonlinear systems. First, we obtain necessary and sufficient conditions for local exponential observers for Lyaupnov stable nonlinear systems. We also show that the definition of local exponential observers can be considerably weakened for neutrally stable nonlinear systems. As an application of our local observer design, we consider a class of nonlinear systems with an input generator (ecosystem) and show that for this class of nonlinear systems, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs.

On the observer design of multi output systems in discrete-time

Proceedings of the 16th IFAC World Congress, 2005, 2005

The paper deals with the equivalence under coordinates change, of a discrete-time nonlinear multi output system to observer canonical forms. Necessary and sufficient conditions for local equivalence to these forms are given.

Observer Design for a Class of Uniformly Observable MIMO Nonlinear Systems with Coupled Structure

Proceedings of the 17th IFAC World Congress, 2008, 2008

A high gain observer is synthesized from a canonical form that characterizes the class of uniformly observable systems. Two main contributions are to be emphasized: the first is related to the considered structure of the canonical form which does not assume a complete triangular structure. That is, each block may contain nonlinearities which depend on the whole state. The second main contribution lies in the simplicity of the observer gain synthesis since the expression of this gain is given and its calibration is reduced to the choice of a single design parameter. Moreover, this involves a design function that has to satisfy a mild condition which is given. Different expressions of such a function are proposed. Of particular interest, it is shown that high gain observers and sliding mode like observers can be derived by considering particular expressions of the design function. An example with simulation results is given for illustration purposes.

Single Output Dependent Observability Normal Form

SIAM journal on control and optimization, 2007

1. Introduction. Since Luenberger's work [9], the design of an observer for observable linear systems with linear outputs has been a well-known concept. In order to use the same observer for nonlinear systems, the so-called observability linearization problem for nonlinear systems was born. ...

Observer design for a class of nonlinear systems

International Journal of Control, 1994

A simple observer is proposed for a large class of multi-output nonlinear systems. The main characteristic of the proposed observer is its implementation and performance tailoring simplicity. Indeed, the gain of this observer does not require the resolution of any dynamical system and is analytically given. Moreover, the performance speci£cation is made through the choice of a unique parameter. The performances of the proposed observer are demonstrated through a real experiment dealing with the estimation of the rotor ¤ux, the motor speed and the load torque in an induction motor.

Transformation the Nonlinear System into the Observer Form: Simplification and Extension

European Journal of Control, 2009

The paper addresses the problem of transforming the discrete-time single-input single-output nonlinear control system into the observer form using the state and output transformations. The necessary and sufficient solvability conditions are formulated in terms of differential one-forms, associated with the input-output equation of the control system. These conditions simplify the existing conditions [10] and extend them for the systems with inputs. The procedures to find the state and output transformations are given.