A geometric approach to differential Hamiltonian systems and differential Riccati equations

TL;DR

This paper provides a geometric framework for understanding differential Hamiltonian systems and Riccati equations, connecting contraction analysis, stability, and control design through tangent bundle lifts.

Contribution

It offers a geometric perspective on control contraction metrics and generalized differential Riccati equations, enhancing theoretical understanding and potential control applications.

Findings

Unified geometric approach to differential Hamiltonian systems

Insight into control contraction metrics and Riccati equations

Connections between differential properties and stability analysis

Abstract

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'.