Extending La Salle´s invariance principle for a class of nonautonomous systems to a sufficient rank condition

The stability of a large class of nonlinear, nonautonomous systems is analysed. In particular, our main contribution is to formulate some easier to verify sufficient conditions for asymptotic stability. To this end, invariance properties of the system are exploited even in the nonautonomous system case in order to derive a rank based asymptotic stability condition. The approach used in this paper, extends LaSalle´s invariance principle by identifying from the structure of the system that suitable limiting equations exist, with reference to which a limit set indeed forms an invariant set for the nonautonomous system. Finally, an illustrative example is used to verify the theoretical analysis.