Observable linear pairs

Abstract

It is well-known that the observabillity rank condition of linear control systems on R-n depends on the pair (A, C) alone. Associated with linear control systems on Lie groups we introduce the notion of linear pairs (X, h). To characterize local and global observability of linear pairs we specialize well known results on the observability of general control systems. In particular, rye use the techniques which appear in [2]. On the other hand, Isidori's algorithm allows to calculate on the co-tangent bundle of G, the Lie algebra of the indistinguishable equivalence class of the identity element.