Orbital Stabilization of Nonlinear Systems via the Immersion and Invariance Technique

Abstract

Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated by some modern applications we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive. The feasibility of our result is illustrated with some classical mechanical engineering and electronics examples.

References in corpus (1)

• Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection

Cited by in corpus (4)

• Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection
• Robust Orbital Stabilization: A Floquet Theory-based Approach
• From gymnastics to virtual nonholonomic constraints: energy injection, dissipation, and regulation for the acrobot
• Path following of a class of underactuated mechanical systems via immersion and invariance-based orbital stabilization