Orbital Stabilization of Nonlinear Systems via the Immersion and Invariance Technique
It provides a new method for orbital stabilization in nonlinear systems, relevant for applications requiring periodic behavior, but the results are preliminary and lack quantitative comparisons.
This paper extends the Immersion and Invariance technique from equilibrium stabilization to orbital stabilization, enabling the generation of attractive periodic solutions in nonlinear systems, demonstrated on mechanical and electronic examples.
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.