**5. Conclusion**

In this chapter, the stabilization problem of complex dynamical network with non-delayed and delayed couplings exchanging randomly has been realized by a new kind of stochastic pinning controller being partially delay-dependent, where the switching between the nondelayed and delayed couplings is modeled by the related coupling matrices containing uncertainties. Different from the traditional pinning methods, the designed pinning controller contains non-delay and delay state terms simultaneously but occurs asynchronously with a certain probability, respectively. Sufficient conditions for the stabilization of complex dynam‐ ical network over topology exchange are derived by the robust method and presented with liner matrix inequities (LMIs). It has been shown that the probability distributions of non-delay and delay states in addition to the bound of such uncertainties play very important roles in the controller design. Moreover, when the probability is inaccessible, a kind of adaptive partially delay-dependent controller is proposed to deal with this general case, where another adaptive control problem in terms of unknown bound is also considered. Finally, the correct‐ ness and feasibility of the proposed method are verified by a numerical simulation.
