An algebraic characterization for observability

This thesis with the title ?An Algebraic Characterization for Observability? consists of three chapters. In the first chapter, manifold structure, Lie group which has a manifold structure and Lie algebra which has a vector space structure are given. Then, relations between Lie groups and Lie algebras via exponential mapping and adjoint representation and the Lie derivative are studied. In the second chapter, definitions of a general control system and observability and the rank condition which is the observability characterization for linear control systems on Rn are given. In the last chapter, observability of linear control systems on a connected Lie group G which is the main research topic is studied. Local and global observability characterizations for this kind of systems with a drift vector field which is an infinitesimal automorphism and an output function which is a kind of projection are given. Results are illustrated by examples. Key words : observability, local observability, indistinguishability relation, infinitesimal automorphism, Lie algebra, ad(X)-invariance.