Observability of general linear pairs

In this work, we deal with the observability of a general linear pair (X, p i(K)) on G which is a connected Lie group with Lie algebra g. By definition , the vector field X belongs to the normalizer of g related to the Lie alge bra of all smooth vector fields on G. K is a closed Lie subgroup of G and p i(K) is the canonical projection of G onto the homogeneous space G/K. We co mpute the Lie algebra of the equivalence class of the identity element, and characterize local and global observability of (X, pi(k)) We extend the we ll-known observability rank condition of linear control systems on R-n and generalize the results appearing in [1]. (C) 1999 Elsevier Science Ltd. All rights reserved.