Remarks on equivalence between full order and reduced order nonlinear observers

Motivated by the fact that, for linear systems, existence conditions for a full order observer and for a reduced order observer are the same, we study relationship between full order and reduced order observers for general nonlinear systems. We employ coordinate transformations for dealing with reduced order observers. By restricting the change of coordinates to be linear, we obtain some equivalence between full order and reduced order observers and relationship between two corresponding error Lyapunov functions.