Stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks

摘要

Lyapunov direct method provides a very effective approach to analyze stability of nonlinear systems. However, the well-known Leibniz rule is not suitable for fractional derivatives, which is the main reason that there are few analytical results on stability of fractional systems. This paper deals with stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks. Applying fractional Lyapunov direct method and S-procedure lemma, several sufficient conditions on stability and a simple condition on global synchronization of a class of fractional singular dynamical networks in terms of linear matrix inequalities are derived. Finally, two simple examples are given to show that our proposed methods are simple and convenient in computation.