Delay-Dependent Stability of Complex Dynamical Networks with Mode-Dependent Parameters and Time Delays

In this paper, the definition of the stochastic stability is proposed for a continuous-time complex dynamical network (CDN), and the stochastic stability of the CDN with uncertain parameters and time delay is investigated. Based on the descriptor model transformation, some delay-dependent sufficient conditions are obtained in terms of linear matrix inequalities (LMIs). An important feature of the results is that both the uncertain parameters and the time delay are subjected to the same continuous-time homogeneous Markov jump process which has discrete and finite state space. Another feature of the results is that the second stability condition is dependent on the difference between upper and lower bound of the delay. A numerical example is presented to show the effectiveness of the theoretical result.