High-gain observers for non-linear systems

State estimation for non-linear dynamic systems is discussed. A high-gain injection from the output variables is used to attenuate to any desired degree, the effect of the non-linear terms on the estimation errors, which can be made arbitrarily small, from a particular observable form. Some Liapunov arguments are used to study the stability properties of the resulting error dynamics. It is shown that any completely observable multi-input multi-output non-linear system, not necessarily linear in the input variables, can be transformed, by means of a change of coordinates depending on the input variables, in such an observable form. In particular, the solvability of partial differential equations is not needed for the design of this transformation.