**New Stabilization of Complex Networks with Nondelayed and Delayed Couplings over Random Exchanges**

Guoliang Wang and Tingting Yan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62504

### **Abstract**

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In this chapter, the stabilization problem of complex dynamical network with nondelayed and delayed couplings is realized by a new kind of stochastic pinning control‐ ler being partially delay dependent, where the topologies related to couplings may be exchanged. The designed pinning controller is different from the traditional ones, whose non-delay and delay state terms occur asynchronously with a certain probability, respectively. Sufficient conditions for the stabilization of complex dynamical network over topology exchange are derived by the robust method and are presented with liner matrix inequities (LMIs). The switching between the non-delayed and delayed cou‐ plings is modeled by the related coupling matrices containing uncertainties. It has shown that the bound of such uncertainties play very important roles in the controller design. Moreover, when the bound is inaccessible, a kind of adaptive partially delay-depend‐ ent controller is proposed to deal with this general case, where another adaptive control problem in terms of unknown probability is considered too. Finally, some numerical simulations are used to demonstrate the correctness and effectiveness of our theoretical analysis.

**Keywords:** complex dynamical network, partially delay-dependent pinning control‐ ler, non-delayed and delayed couplings, robust method, adaptive control
