Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 57, Issue 10, Pages 2644-2650Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2012.2190179
Keywords
Dynamical networks; Gronwall's inequality; Jenson integral inequality; sampled-data control; stochastic sampling; synchronization control
Funding
- Engineering and Physical Sciences Research Council (EPSRC) of the UK [GR/S27658/01]
- Royal Society of the UK
- National Natural Science Foundation of China [61028008, 60974030, 61134009, 61104125]
- National 973 Program of China [2009CB320600]
- Fundamental Research Funds for the Central Universities
- Alexander von Humboldt Foundation of Germany
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This technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme.
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