Analysis and Control of the Hopf bifurcation

In this Ph.D. thesis a rigorous theory for the local analysis and control of the Hopf bifurcation is developed. Moreover, some original ideas oriented to the analytical approach are introduced as well, in order to provide exact mathematical tools, which turn out actually applicable to real world problems. These results are settled in the frequency approach to the study of the Hopf bifurcation and they are developed by using second-order harmonic balance techniques and controller normal forms. Those tools may turn out useful in the standard Hopf bifurcation control problems, providing a more manageable and less conservative analytical approach.