Algebraic observability of nonlinear differential algebraic systems with geometric index one

Electro mechanical systems are naturally expressed as differential and algebraic equations because the systems are constrained by the Kirchhoff's law. In order to examine local observability of such systems, this paper introduces concepts called algebraic observability and regular trajectory. Algebraic observability can be examined by elementary matrix operations of a certain polynomial matrix derived from a given system. Hence in order to check algebraic observability of a given system, it is possible to apply computer algebra such as Mathematica and Maple. Through a simple circuit model, it is shown that one can easily examine local observability by using the concepts of algebraic observability and regular trajectory, even if a conventional method for checking local observability is not applicable.