A linear matrix inequality approach for the position control of a double-side impact mechanical oscillator via a state feedback law

Abstract

This paper proposes a state-feedback controller using Linear Matrix Inequality (LMI) method for the position control of an impact oscillator with asymmetric double-side endstops. The main idea lies in the use of the S-procedure Lemma to solve the stabilization problem requiring solving two Bilinear Matrix Inequality (BMIs). Nevertheless, such problem with BMI constraints is NP-hard and then it is difficult to obtain traceable solutions. To solve such problem, we transform these BMIs into LMIs through the Schur complement Lemma and the Matrix Inversion Lemma. The simulations results show that the impact oscillator is controlled and hence kept in the desired position.