Differential analysis of nonlinear systems: revisiting the pendulum example

Abstract

Differential analysis aims at inferring global properties of nonlinear behaviors from the local analysis of the linearized dynamics. The paper motivates and illustrates the use of differential analysis on the nonlinear pendulum model, an archetype example of nonlinear behavior. Special emphasis is put on recent work by the authors in this area, which includes a differential Lyapunov framework for contraction analysis and the concept of differential positivity.

12 pages, 14 figures. Tutorial paper for the 53rd IEEE Conference on Decision and Control, 2014

References in corpus (2)

• Symmetries, Stability, and Control in Nonlinear Systems and Networks
• On differential passivity of physical systems

Cited by in corpus (2)

• Monotonicity on homogeneous spaces
• Generic behavior of differentially positive systems on a globally orderable Riemannian manifold