Lageman, ChristianTrumpf, JochenMahony, Robert2015-12-100018-9286http://hdl.handle.net/1885/59072This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of two dynamical systems is specialized to systems on Lie groups. For invariant systems this leads to a general factorization theorem of a nonlinear observer into a synchronous (internal model) term and an innovation term. The synchronous term is fully specified by the system model. We propose a design methodology for the innovation term based on gradient-like terms derived from invariant or non-invariant cost functions. The resulting nonlinear observers have strong (almost) global convergence properties and examples are used to demonstrate the relevance of the proposed approach.Keywords: Design Methodology; Factorization theorems; Finite dimensional; Global convergence; Gradient systems; Gradient-like; Internal models; Invariant dynamics; Invariant systems; Kinematic systems; Lie group; Non-linear observer; Nonlinear state; System models; Gradient systems; Lie groups; Observers; Synchrony201010.1109/TAC.2009.20349372016-02-24