Existence Conditions for ODE Functional Observer Design of Descriptor Systems

This letter studies the design of functional observers for linear time-invariant descriptor systems which are not necessarily square and regular. A novel characterization for the existence of functional observers is presented. The observer is realized by a system of ordinary differential equations (ODEs). The existence of ODE observers is proved by means of a set of simple rank conditions on the system coefficient matrices. The proposed conditions are less restrictive than the existing ones. The derivation is purely algebraic, and the algorithm is illustrated by designing an observer-based controller.

Automated summary

This letter studies the design of functional observers for linear time-invariant descriptor systems which are not necessarily square and regular. A novel characterization for the existence of functional observers is presented using a set of simplified rank conditions on the system coefficient matrices. The proposed conditions are less restrictive than the existing ones. The derivation is purely algebraic and an observer-based controller is designed as an illustration.