Pinning Synchronization of Directed Networks with Markovian Jump and Nonlinear Perturbations* *This work was jointly supported by CityU under a research grant (7002208).

Abstract In this paper, synchronization of a directed network with Markovian jump (DNMJ) and nonlinear perturbations is considered. By analyzing the structure of the network, a pinning control scheme is given to ensure the synchronization of all nodes in a DNMJ. Finally, an example is provided to illustrate the effectiveness of the gained criterion.

[1]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  O. Costa Linear minimum mean square error estimation for discrete-time Markovian jump linear systems , 1994, IEEE Trans. Autom. Control..

[3]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[4]  Dongjun Lee,et al.  Stable Flocking of Multiple Inertial Agents on Balanced Graphs , 2007, IEEE Transactions on Automatic Control.

[5]  A. Willsky,et al.  Discrete-time Markovian-jump linear quadratic optimal control , 1986 .

[6]  Marios Mavronicolas,et al.  Efficient Bufferless Packet Switching on Trees and Leveled Networks ∗ , 2005 .

[7]  Jinde Cao,et al.  Global synchronization in arrays of delayed neural networks with constant and delayed coupling , 2006 .

[8]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[9]  Yingmin Jia,et al.  Distributed robust Hinfinity consensus control in directed networks of agents with time-delay , 2008, Syst. Control. Lett..

[10]  Han-Chieh Chao,et al.  Jumping ant routing algorithm for sensor networks , 2007, Comput. Commun..

[11]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[12]  Zidong Wang,et al.  Exponential synchronization of complex networks with Markovian jump and mixed delays , 2008 .

[13]  J. Liang,et al.  Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

[14]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[15]  M. Cross,et al.  Pinning control of spatiotemporal chaos , 1997, chao-dyn/9705001.

[16]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[17]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[18]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[19]  James Lam,et al.  H∞ model reduction of Markovian jump linear systems , 2003, Syst. Control. Lett..

[20]  Daniel W. C. Ho,et al.  Globally exponential synchronization in an array of asymmetric coupled neural networks , 2007 .

[21]  Jinde Cao,et al.  Synchronization analysis of singular hybrid coupled networks , 2008 .

[22]  Mike Casey,et al.  The Dynamics of Discrete-Time Computation, with Application to Recurrent Neural Networks and Finite State Machine Extraction , 1996, Neural Computation.

[23]  Ji Xiang,et al.  On the V-stability of complex dynamical networks , 2007, Autom..