Probability-dependent H∞ synchronization control for dynamical networks with randomly varying nonlinearities

In this paper, the H∞ synchronization control problem is investigated 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 by a randomly varying conditional probability distribution. 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 the simultaneous presence of randomly varying nonlinearities and external energy bounded disturbances. Except for constant gains, the desired controllers are also composed of time varying parameters, i.e., the time varying switching probability and therefore less conservatism will be resulted comparing with traditional controllers. In virtue of semi-definite programming method, controller parameters are derived in terms of the solutions to a series of linear matrix inequalities (LMIs) that can be easily solved by the Matlab toolboxes. Finally, a simulation example is exploited to illustrate the effectiveness of the proposed control strategy.