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Nonlinear adaptive observer for a parameter affine linearizable system

The nonlinear adaptive observer design problem is studied for a nonlinear system that can be transformed into a parameter affine linear system using output-dependent input transformation. A necessary and sufficient condition is given to transform a given nonlinear system into a parameter affine linear system. Once a nonlinear system is transformed into a parameter affine linear system, various linear adaptive observer design techniques can be used. A necessary and sufficient condition is given for the transformed parameter affine linear system to be observable under the relative degree assumption of the nonlinearity containing parameters. It is also shown that the observability and controllability of the parameter affine linear system are invariant under the coordinate change that transforms the original nonlinear system into the parameter affine linear system under some assumptions.