Multiple Time Scalings of a Multi-Output Observer Form

Time scalings in the multi-output observer form for uncontrolled nonlinear continuous-time systems are considered in this technical note. It is the multi-output version of an existing single-input result. Time scaling broadens the class of systems which admits an exact error linearization observer design by including time scaling transformations. The existence conditions of the time scaling transformation and the change of state coordinates to time-scaled observer form are provided.