A geometric approach to differential Hamiltonian systems and differential Riccati equations

Motivated by research on contraction analysis and incremental stability/stabilizability the study of `differential properties´ has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle of the state space manifold have been employed for a geometric approach to differential passivity and dissipativity. In the same vein, the present paper aims at a geometric underpinning and elucidation of recent work on `control contraction metrics´ and `generalized differential Riccati equations´.