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ℋ∞ synchronization control for dynamical networks: A probability-dependent gain-scheduled method

In this paper, the ℋ∞ synchronization control problem is concerned for a class of dynamical networks with randomly varying nonlinearities. The time varying nonlinearities of each node are modelled to be randomly switched between two different nonlinear functions by utilizing a Bernoulli distributed variable sequence specified. A probability-dependent gain scheduling method is adopted to handle the time varying characteristic of the switching probability. Attention is focused on the design of a sequence of gain-scheduled controllers such that the controlled networks are exponentially mean-square stable and the ℋ∞ synchronization performance is achieved. In virtue of semi-definite programming method, controllers parameters are derived in terms of the solutions to a series of linear matrix inequalities (LMIs). Finally, a simulation example is exploited to illustrate the effectiveness of the proposed control strategy.