Nonlinear system immersion, observers and finite-dimensional filters
The authors consider nonlinear stochastic systems with parameter excitation by Gaussian white noise and with nonlinear observations additively corrupted by Gaussian white noise as well as the deterministic counterparts of such systems. They give necessary and sufficient conditions for these systems to be ''immersible'' into appropriate linear observable systems. They prove that being immersible is sufficient for the deterministic systems considered to admit observers and for the stochastic systems considered to admit exact finite-dimensional filters. Compared with known results, the corresponding classes of systems are considerably extended by this.
scientific article; zbMATH DE number 3952602
scientific article