Transverse Dynamics and Regions of Stability for Nonlinear Hybrid Limit Cycles
Optimization and Control
2010-10-13 v1
Abstract
This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from the linearization of the transverse dynamics construct a quadratic candidate Lyapunov function; (3) search for a new Lyapunov function verifying maximal regions of orbital stability via iterated of sum-of-squares programs. The construction of the transverse dynamics is novel, and valid for a broad class of nonlinear hybrid systems. The problem of stabilization of unstable limit cycles will also be addressed, and a solution given based on stabilization of the transverse linearization.
Keywords
Cite
@article{arxiv.1010.2241,
title = {Transverse Dynamics and Regions of Stability for Nonlinear Hybrid Limit Cycles},
author = {Ian R. Manchester},
journal= {arXiv preprint arXiv:1010.2241},
year = {2010}
}