Master-slave controlled synchronization to control chaos in an impact mechanical oscillator

This work aims at controlling chaos exhibited in the impulse hybrid dynamics of a 1DOF impact mechanical oscillator by achieving a master-slave controlled synchronization. Our objective is to synchronize the motion of a chaotic slave impact oscillator with that of a periodic master impact oscillator via an external control input. The master-slave synchronization problem is reformulated as the stabilization of the synchronization error by means of a state-feedback controller. For the design of the control input, we deal only with the linear dynamics of the two systems during their oscillation phase. Our fundamental approach hinges mainly on the use of the S-procedure in order to reduce the conservatism of the classical Lyapunov approach. We employ also the Schur complement and the Matrix Inversion Lemma in order to transform a BMI into a LMI. We show the effectiveness of the proposed method for the control of chaos by applying the designed control input to the chaotic impact oscillator.