Robust master-slave synchronization of chaos in a one-sided 1-DoF impact mechanical oscillator subject to parametric uncertainties and disturbances

Abstract

This paper addresses the problem of robust master-slave synchronization of chaos in a 1-DoF impact mechanical oscillator with a single rigid constraint. The master is considered to be with nominal parameters, whereas the slave impacting system is considered to be subject to polytopic parametric uncertainties and disturbances. We adopt a state-feedback controller for the robust stabilization of the master-slave synchronization error and the Linear Matrix Inequality (LMI) approach for the design of stability conditions. We use the S-procedure Lemma in order to only consider the regions within which the two impacting systems evolve. Thus, the stability conditions are formulated in terms of Bilinear Matrix Inequalities (BMIs). Via some technical Lemmas and congruence transformations, we transform these BMIs into LMIs, which are numerically traceable. An improved LMI-based optimization problem is proposed to solve the problem of high gains of the controller. Finally, the robustness of the proposed state-feedback feedback controller towards parametric uncertainties and disturbances is presented through simulation results showing then the master-slave synchronization of chaos in the one-sided 1-DoF impact mechanical oscillator.