Master-Slave Tracking of a Rigid Double-Side SDOF Impact Mechanical Oscillator Using Polyhedral Sets

This research study proposes a design methodology of a master-slave state-feedback controller based on the linear matrix inequality (LMI) method for some class of complex robotic systems, which is the single degree-of-freedom (SDOF) impacting mechanical oscillator with two asymmetric rigid double-side constraints. To deal with the stabilization problem, we employ the S-procedure lemma that generates four bilinear matrix inequalities (BMIs). By virtue of the matrix inversion lemma and the Schur complement, these obtained BMIs are therefore transformed into LMIs. The results obtained by the simulation show that the slave mechanical impact oscillator is well controlled and hence track the desired trajectory of the master.