Reduced-Order Dynamic Observer Error Linearization

Abstract For an unforced nonlinear single output system, we propose a new approach to observer error linearization called reduced-order dynamic observer error linearization (RDOEL), which is a modified version of dynamic observer error linearization (DOEL). While RDOEL also has an auxiliary dynamics and a generalized output injection like DOEL, it offers a lower dimensional observer than DOEL, and allows a complete constructive algorithm in contrast to DOEL when the auxiliary dynamics is a chain of integrators. For RDOEL whose auxiliary dynamics is a chain of integrators (RDOELI), we provide a complete constructive algorithm which presents not only a coordinate transformation between the original system and a nonlinear observer canonical form, but also the minimum number of integrators needed to perform RDOELI. Moreover, we show that if the original system is of dimension n , then the minimum number of integrators is less than or equal to n –- 2. In order to describe our algorithm well, we present an example that the auxiliary dynamics is a chain of two integrators.