Further discussion on a Block Triangular Observer Form

This paper discusses the existence conditions of a block triangular observer form (BTOF) for unforced nonlinear multi-output systems. The BTOF is originally presented in (J. Rudolph and M. Zeitz) to allow an established exact error linearization observer design method to be generalized to a larger class of multi-output systems. Its existence conditions are investigated in (J. Rudolph and M. Zeitz, 1994), (Y. Wang and A. Lynch, 2008). Different from the approach employed in previous works, where the existence conditions of a lower dimension state transformation putting certain subsystem into BTOF is discussed separately, this note considers the state transformation of the entire system at a time. The assumption that the outputs and states of the lower subsystems are treated as parameters, which is made in the previous works to simplify the derivation of the existence conditions, is removed. New necessary and sufficient conditions are given for the BTOF.