Multi-output dependent observability normal form

This article gives a sufficient condition which guarantees the existence of a reference frame in which a multi-output nonlinear system is linearizable with a linear part depending on its outputs. Our method is based on the design of a reference frame associated with nonlinear observable systems. Moreover, we give a generalization of the result obtained in D. Boutat, G. Zheng, J.P. Barbot, Observer error linearization multi-output depending, in: Proc. of IEEE CDC 06, 2006] and G. Zheng, D. Boutat, J.P. Barbot, Single output-dependent observability normal form, SIAM Journal on Control and Optimization 46 (6) (2007)]. And some examples are given in order to illuminate our thinking.