A Canonical form of Completely Uniformly Locally Weakly Observable Multi-output Nonlinear Systems

The observability of nonlinear systems was considered in this note. First, we reviewed the definitions and relations of observable, locally observable, weakly observable, locally weakly observable, uniformly locally weakly observable and completely uniformly locally weakly observable. Then, a sufficient condition under which a multi-output nonlinear system is completely uniformly locally weakly observable was given. The sufficient condition becomes necessary and sufficient condition when the system is single-output. We also gave a canonical form of these multi-output systems. In the end, an example illustrated how to use the given sufficient conditions to determine whether a nonlinear system is completely uniformly locally weakly observable.