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This study presents the synchronisation of two chaotic systems, namely drive and response chaotic systems, using polynomial controllers. Both output and full state-feedback polynomial controllers are proposed, respectively, to drive the system states of the response system to approach those of the drive one. The system stability of the overall system is investigated by the Lyapunov stability theory. Stability conditions in terms of sum of squares (SOS) are derived to aid the design of the feedback gains of the polynomial controllers. By satisfying the SOS-based stability conditions, chaotic synchronisation is achieved with system performance guaranteed by an H∞ performance function. Simulation examples are given to illustrate the merits of the proposed polynomial control approach.