Robust stability of a class of nonlinear oscillators

Robust analysis of a class of synchronized second order driven oscillators is studied in this work. A dynamical system is constructed from the synchronization error. Such system is stabilized around origin via PI-controller. The goals are: (i) To show that synchronization is locally robustly stable and (ii) There exists a control parameter such that synchronization remains against uncertainties. Since the synchronization problem is solved from stabilization of synchronization error at origin, results provide a quantitative measure of robustness margins, via ℋ_∞-norm