Lower bounds for the stability degree of periodic solutions in forced nonlinear systems

In this paper the problem of local exponential stability of periodic orbits in a general class of forced nonlinear systems is considered. Some lower b ounds for the degree of local exponential stability of a given periodic sol ution are provided by mixing results concerning the analysis of linear time -varying systems and the real parametric stability margin of uncertain line ar time-invariant systems. Although conservative with respect to the degree of stability obtainable via the Floquet-based approach, such lower bounds can be efficiently computed also in cases where the periodic solution is no t exactly known and the design of a controller ensuring a satisfactory tran sient behavior is the main concern. The main features of the developed appr oach are illustrated via two application examples.