Exponential stability of a competitive Lotka-Volterra system with delays

In this paper, the exponential stability of a two-species competitive Lotka-Volterra system with discrete delays has been studied. By constructing appropriate Lyapunov functional and using the linear matrix inequality (LMI) optimization approach, a series of sufficient criteria is obtained which ensure the exponential stability of the positive equilibrium of the given Lotka-Volterra system. The results are new and improve some earlier work. An illustrative example is given to demonstrate the effectiveness of the obtained results.