Embedding observers for polynomial dynamical systems

Observers are used in a variety of control applications. This includes estimating a systems state, system parameters, or fault detection. Systematic observer design is applicable on basis of the observer- or observability normal form. While the former normal form is preferable because of the easier observer design, it exists for a smaller subset of dynamical systems than the latter one. For nonlinear systems the vector field in the observability normal form may possess singularities or may fail a Lipschitz condition. This can sometimes be avoided by embedding the system in a higher-dimensional state space. In this contribution this embedding and its implications are discussed for polynomial multiple input or output systems.

Automated summary

Observers are used in control applications to estimate system state, parameters, or detect faults. Systematic observer design is based on observer or observability normal form. The former is preferred for easier design, but is applicable to a smaller subset of dynamical systems compared to the latter. Nonlinear systems may have singularities or fail Lipschitz condition in the observability normal form, which can be avoided by embedding the system in a higher-dimensional state space. This paper discusses this embedding and its implications for polynomial multiple input or output systems.