Immersion technique for nonlinear observer design

This paper investigates when n dimensional nonlinear systems can be immersed into n +m dimensional nonlinear systems in nonlinear observer form, and derives a necessary and sufficient condition. We also present an algorithm to check the immersibility. In general, one can check the immersibility by solving partial differential equation with m+1 unknowns rather than solving one with n+m unknowns. When m≤n/2, one can check the immersibility by direct calculation.