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.