Time scaling of a multi-output observer form

This paper considers the time scaling of a multi-output observer form (TOF) for uncontrolled nonlinear continuous-time systems. It is the multi-output version of an existing single-output result. Time scaling broadens the class of systems which admits an exact error linearization observer design by including time scaling functions (TSFs). Two types of TSFs are considered and the corresponding existence conditions of the time scaling transformation and the change of state coordinates to a TOF are provided. The necessary and sufficient conditions on TSFs to preserve the global exponential stability of the error dynamics are presented.