Algebraic Controllability and Observability of Nonlinear Differential Algebraic Systems with Geometric Index One

Abstract

The paper introduces concepts called algebraic controllability and algebraic observability for nonlinear differential algebraic systems with geometric index one. To characterize them, controllable trajectory and observable trajectory are also introduced. It is shown that every linearized algebraically controllable system along any (periodic) controllable trajectory is (uniformly) completely controllable. As a dual result, it is shown that every linearized algebraically observable system along any (periodic) observable trajectory is (uniformly) completely observable.